Take-home Exercise 2: Applied Spatial Interaction Models: A case study of Singapore public bus commuter flows

Published

December 9, 2023

Modified

December 17, 2023

1 Background

Urban commuters on the morning and traveling to work face complex mobility challenges, prompting questions about the impacts of public bus service removal along their routes. Traditional methods like commuter surveys are costly, time-consuming, and often result in outdated information. With the digitization of city-wide infrastructure and the widespread use of GPS on the vehicles and SMART cards in public transport, vast geospatial data sets are generated. However, the rapid growth of this data has overwhelmed planners, hindering their ability to transform it into meaningful insights and impacting the return on investment in data collection.

2 The Data

2.1 Open Government Data

For the purpose of this assignment, data from several open government sources will be used:

  • Passenger Volume by Origin Destination Bus Stops, Bus Stop Location, Train Station and Train Station Exit Point, just to name a few of them, from LTA DataMall.

  • Master Plan 2019 Subzone Boundary, HDB Property Information, School Directory and Information and other relevant data from Data.gov.sg.

  • hexagon, a hexagon layer of 375m (this distance is the perpendicular distance between the centre of the hexagon and its edges.) should be used to replace the relative coarse and irregular Master Plan 2019 Planning Sub-zone GIS data set of URA.

2.2 Specially collected data

  • Business, entertn, F&B, Leisure&Recreation are geospatial data sets of the locations of business establishments, entertainments, food and beverage outlets, leisure and recreation centres compiled for case study of Singapore public bus commuter flows. They are available on in the geospatial folder to Take-home Exercise 2 data folder.

  • HDB: This data set is the geocoded version of HDB Property Information data from data.gov. The data set is prepared using September 2021 data.

2 Getting Started

For the purpose of this study, 10 r packages will be used. They are:

  1. tmap is a package for creating thematic maps. It provides a flexible and powerful framework for visualizing spatial data.

  2. sf is an R package for simple features, which provides a standard way to encode spatial vector data.

  3. DT is a package that extends the data.table package and provides functions to create interactive data tables in R Markdown documents and Shiny web applications.

  4. stplanr is a package for sustainable transport planning. It offers functions for transport planning and modeling, particularly with spatial data.

  5. performance package is often associated with the yardstick package and provides functions for model performance metrics, such as RMSE, MAE, etc.

  6. sp is a package for handling and analyzing spatial data. It is one of the foundational packages for spatial data manipulation and analysis in R.

  7. ggpubr is a package for creating beautiful and customizable ggplot2-based plots for publication.

  8. tidyverse is a collection of R packages, including dplyr, ggplot2, tidyr, and others. It promotes a tidy data workflow and provides a consistent set of functions for data manipulation and visualization.

  9. corrplot is a package for visualizing correlation matrices using colored plots. It helps in understanding the relationships between variables in a dataset.

  10. yardstick is a package for measuring model performance. It provides functions for computing various metrics, such as accuracy, precision, recall, and others.

The code chunk below installs and loads the various packages.

Code 
pacman::p_load(tmap, sf, DT, stplanr,   
               performance, sp,
               ggpubr, tidyverse, corrplot,
               yardstick)

3 Data Preparation

3.1 Importing the OD data

Firstly, we will import the Passenger Volume by Origin Destination Bus Stops data set downloaded from LTA DataMall by using read_csv() of readr package.

Code 
odbus <- read_csv("data/aspatial/origin_destination_bus_202308.csv",show_col_types = FALSE)

Let use display the odbus tibble data table by using the code chunk below.

Code 
glimpse(odbus)
Rows: 5,709,512
Columns: 7
$ YEAR_MONTH          <chr> "2023-08", "2023-08", "2023-08", "2023-08", "2023-…
$ DAY_TYPE            <chr> "WEEKDAY", "WEEKENDS/HOLIDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR       <dbl> 16, 16, 14, 14, 17, 17, 17, 17, 7, 17, 14, 10, 10,…
$ PT_TYPE             <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE      <chr> "04168", "04168", "80119", "80119", "44069", "4406…
$ DESTINATION_PT_CODE <chr> "10051", "10051", "90079", "90079", "17229", "1722…
$ TOTAL_TRIPS         <dbl> 7, 2, 3, 10, 5, 4, 3, 22, 3, 3, 7, 1, 3, 1, 3, 1, …

A quick check of odbus tibble data frame shows that the values in OROGIN_PT_CODE and DESTINATON_PT_CODE are in numeric data type. Hence, the code chunk below is used to convert these data values into character data type.

Code 
odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE)

3.2 Extracting the study data

For this take home exercise, we will extract commuting flows on weekday and between 6 and 9 o’clock.

Code 
odbus6_9 <- odbus %>%
  filter(DAY_TYPE == "WEEKDAY") %>%
  filter(TIME_PER_HOUR >= 6 &
           TIME_PER_HOUR <= 9) %>%
  group_by(ORIGIN_PT_CODE,
           DESTINATION_PT_CODE) %>%
  summarise(TRIPS = sum(TOTAL_TRIPS))

Table below shows the content of odbus6_9

Code 
datatable(odbus6_9)

4 Working with Geospatial Data

For the purpose of this exercise, three geospatial data will be used. They are:

  • Bus Stop Location from LTA DataMall. It provides information about all the bus stops currently being serviced by buses, including the bus stop code (identifier) and location coordinates.

  • MPSZ-2019: This data provides the sub-zone boundary of URA Master Plan 2019.

  • hexagon, a hexagon layer of 375m (this distance is the perpendicular distance between the centre of the hexagon and its edges.) should be used to replace the relative coarse and irregular Master Plan 2019 Planning Sub-zone GIS data set of URA.

4.1 Importing geospatial data

Code 
busstop <- st_read(dsn = "data/geospatial",
                   layer = "BusStop") %>%
  st_transform(crs = 3414)
Reading layer `BusStop' from data source 
  `C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21

Let’s take a look at the location of bus stops in Singapore:

Code 
plot(busstop['BUS_STOP_N'])

Code 
mpsz <- st_read(dsn = "data/geospatial",
                   layer = "MPSZ-2019") %>%
  st_transform(crs = 3414)
Reading layer `MPSZ-2019' from data source 
  `C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84

Let’s take a look at the map of subzone in Singapore.

Code 
plot(mpsz['SUBZONE_C'])

4.2 Create Hexagon grid (honeycomb)

For this exercise purpose, we need to create an analytical hexagon data of 375m. (this distance is the perpendicular distance between the centre of the hexagon and its edges)

The following code creates a hexagon grid, associates bus stops with hexagons, and filters out hexagons without any bus stops. The resulting bs_num data frame contains information about hexagons with at least one bus stop.

Code 
area_honeycomb_grid = st_make_grid(busstop,cellsize = 750, what = "polygons", square = FALSE)

honeycomb_grid_sf = st_sf(area_honeycomb_grid) %>%
  mutate(grid_id = 1:length(lengths(area_honeycomb_grid)))
honeycomb_grid_sf$num_bs = lengths(st_intersects(honeycomb_grid_sf, busstop))


bs_num = filter(honeycomb_grid_sf, num_bs > 0)

Let’s take a look at the hexagon grid:

Code 
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
  tm_borders(alpha=0.7,col = "white")+
  tm_polygons("darkgrey") +
tm_shape(bs_num) +
  tm_fill("num_bs",alpha=0.8,palette = "Greens")+
  tm_polygons()

5 Geospatial data wrangling

5.1 Combining Busstop and Hexagon grid

After running this code, honeycomb_grid will be a data frame containing information about bus stops that fall within the hexagons, including the bus stop ID (BUS_STOP_N), the hexagon ID (grid_id), and the number of bus stops within that hexagon (num_bs).

Code 
honeycomb_grid <- st_intersection(busstop, bs_num) %>%
  select(BUS_STOP_N, grid_id,num_bs) %>%
  st_drop_geometry()
honeycomb_grid 
     BUS_STOP_N grid_id num_bs
3269      25059      23      1
2570      25751      44      1
254       26379      46      2
2403      26369      46      2
2829      25741      66      1
1715      26399      67      4
2827      25719      67      4
2828      25711      67      4
4203      26389      67      4
1565      26299      68      1
2897      25761      86      1
2564      25729      87      1
1072      26451      88      4
2781      25701      88      4
2782      25709      88      4
4512      26461      88      4
2672      26279      89      2
2707      26289      89      2
4239      26241      90      1
1464      26409     109      3
2752      25631     109      3
5156      26419     109      3
729       26311     110      2
5027      26321     110      2
1502      26251     111      5
1700      26259     111      5
1875      26349     111      5
2060      26269     111      5
2629      26261     111      5
2487      26209     112      2
3550      26201     112      2
2823      25771     128      1
2678      25801     129      1
981       26441     130      5
2750      25611     130      5
2751      25621     130      5
2896      25651     130      5
3647      26431     130      5
1778      26331     131      3
2746      25599     131      3
2747      25591     131      3
2573      26081     132      6
2578      26071     132      6
2623      26089     132      6
2740      25569     132      6
2843      26249     132      6
4931      26079     132      6
1911      25459     133      7
2172      25469     133      7
2535      25451     133      7
2769      25689     133      7
2770      25681     133      7
3614      25461     133      7
4460      25449     133      7
749       25429     134      1
1589      25781     150      2
2893      25791     150      2
2825      25661     151      5
2826      25669     151      5
4158      26221     151      5
4240      26429     151      5
5070      26211     151      5
2748      25601     152      2
2749      25609     152      2
2739      25561     153      3
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2742      25571     153      3
136       25391     154      8
366       25399     154      8
566       26099     154      8
2784      26101     154      8
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2861      25691     154      8
4376      26109     154      8
4437      26141     154      8
2293      25439     155      5
3343      25499     155      5
3894      25491     155      5
4188      25431     155      5
4643      25441     155      5
2238      25269     156      1
2689      25641     172      2
2768      25671     172      2
356       26069     174      3
2562      26061     174      3
2837      26059     174      3
85        25509     175     11
813       25479     175     11
915       25471     175     11
1081      25501     175     11
1241      25071     175     11
2088      25519     175     11
2731      24711     175     11
2732      24719     175     11
3093      25811     175     11
3419      25819     175     11
5039      25511     175     11
308       25411     176      5
840       25259     176      5
2525      25421     176      5
5057      25009     176      5
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1471      26031     195      5
3553      26049     195      5
4073      26051     195      5
4074      26041     195      5
4075      26039     195      5
679       26151     196      8
738       25079     196      8
1382      25069     196      8
1435      25061     196      8
1804      25389     196      8
2737      25551     196      8
2738      25559     196      8
4833      25381     196      8
1605      25231     197      2
4048      25249     197      2
769       24621     215      2
5031      24629     215      2
325       26131     216      9
1992      26171     216      9
2488      26161     216      9
2571      26029     216      9
2572      26019     216      9
2729      24701     216      9
2730      24709     216      9
3495      26021     216      9
3691      26011     216      9
13        25099     217     10
203       25119     217     10
632       25091     217     10
1219      25101     217     10
2733      25539     217     10
2734      25531     217     10
2735      25541     217     10
2736      25549     217     10
5062      25109     217     10
5073      25111     217     10
1638      26119     237      4
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3877      26111     237      4
4221      26121     237      4
58        25379     238      7
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2743      25589     238      7
3552      25371     238      7
3639      25361     238      7
3879      25359     238      7
4234      25351     238      7
221       25221     239      2
2316      25239     239      2
1269      24431     257      4
2100      24531     257      4
2126      24619     257      4
2222      24611     257      4
1331      25321     258      7
2341      25339     258      7
2824      25821     258      7
3789      25329     258      7
3973      25341     258      7
4150      25331     258      7
4935      25349     258      7
3825      25151     259      4
4049      25229     259      4
4363      25129     259      4
4407      25121     259      4
538       24559     278      5
801       24541     278      5
2329      24549     278      5
3187      24539     278      5
5130      24421     278      5
422       24209     279     10
509       24521     279     10
1296      24681     279     10
1527      24529     279     10
3363      24601     279     10
4208      24609     279     10
4209      24691     279     10
4238      24199     279     10
4507      24689     279     10
4518      24699     279     10
575       25161     280      7
967       25171     280      7
1820      25189     280      7
1988      25169     280      7
4226      25181     280      7
4331      25179     280      7
4753      25219     280      7
4806      24391     298      1
2541      24189     299      6
2839      24671     299      6
3901      24441     299      6
4483      24661     299      6
4715      24669     299      6
4925      24679     299      6
2040      25191     300      7
3162      24519     300      7
3785      24511     300      7
3878      25199     300      7
3979      24219     300      7
4921      25201     300      7
5157      25209     300      7
328       24379     320      5
2428      24411     320      5
3804      24451     320      5
3811      24369     320      5
3955      24401     320      5
3815      24301     321      2
4230      24641     321      2
332       24501     322      3
755       24581     322      3
3640      24509     322      3
267       24461     340      5
1624      24349     340      5
1723      24359     340      5
4272      24341     340      5
4421      24351     340      5
1128      24169     341      6
2838      24381     341      6
4116      24339     341      6
4144      24179     341      6
4530      24331     341      6
4837      24389     341      6
1112      24229     342      3
1955      24021     342      3
4085      24239     342      3
453       24089     363      3
3493      24651     363      3
3636      24299     363      3
530       24571     364      8
1495      24149     364      8
1960      24029     364      8
2397      24599     364      8
2548      24139     364      8
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3613      24129     364      8
4608      24499     364      8
1585      23239     383      6
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3485      24289     383      6
3587      23229     383      6
3792      23221     383      6
3960      23231     383      6
93        24011     384      5
386       24249     384      5
1704      24269     384      5
2520      24259     384      5
4175      24639     384      5
1396      24049     385      2
1812      24041     385      2
2550      23311     404      4
2605      23301     404      4
3908      23291     404      4
4205      23321     404      4
2201      24279     405      7
3536      23449     405      7
3540      23441     405      7
3963      23349     405      7
3975      23359     405      7
4200      23341     405      7
4649      23351     405      7
1742      24019     406      9
3638      23499     406      9
3976      23491     406      9
4014      24009     406      9
4018      23519     406      9
4149      24159     406      9
4484      23489     406      9
4598      23379     406      9
4603      23371     406      9
1132      27231     407      2
3288      27241     407      2
798       27211     408      6
1294      27221     408      6
1966      27051     408      6
2014      27031     408      6
3092      27219     408      6
3428      27041     408      6
1005      23439     425      5
1445      23249     425      5
3959      23281     425      5
4187      23431     425      5
4229      23241     425      5
584       24631     426      9
672       23199     426      9
1945      23479     426      9
2663      23191     426      9
3855      23471     426      9
3881      23369     426      9
3888      23031     426      9
4196      23361     426      9
4923      23039     426      9
621       23081     427      4
1135      23089     427      4
2325      23079     427      4
3165      23071     427      4
3150      27251     428      1
2587      27021     429      2
2941      27071     429      2
652       23411     446      4
3489      23429     446      4
3882      23419     446      4
4847      23421     446      4
1141      23251     447      4
3479      23261     447      4
3796      23259     447      4
3904      23269     447      4
11        23151     448      9
1120      23141     448      9
1208      23121     448      9
1393      23159     448      9
1760      23129     448      9
2216      23149     448      9
2223      23139     448      9
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1500      27291     450      5
1825      27069     450      5
2622      27311     450      5
3432      27061     450      5
3436      27209     450      5
4186      31009     452      1
170       23029     468      6
661       23211     468      6
1058      23219     468      6
4810      23021     468      6
4819      23201     468      6
4820      23209     468      6
628       23049     469      6
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1429      23061     469      6
2545      23059     469      6
3989      23069     469      6
5068      23041     469      6
1845      27131     470      7
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2565      27271     470      7
3728      27139     470      7
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4089      27261     470      7
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2294      27189     471      4
2438      27199     471      4
3438      27011     471      4
4808      27181     471      4
503       31121     472      2
1329      31129     472      2
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1644      23391     488      4
2188      23401     488      4
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4895      23279     489      2
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639       23109     490     13
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1710      23171     490     13
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3646      23161     490     13
3780      23181     490     13
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3807      23101     490     13
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94        27149     491      9
2665      27519     491      9
4023      27511     491      9
4600      27501     491      9
4601      27529     491      9
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5045      27159     491      9
686       31011     493      4
1075      31029     493      4
4393      31021     493      4
4944      31019     493      4
157       31059     494      6
968       31149     494      6
969       31141     494      6
1194      31051     494      6
1314      31139     494      6
2560      31131     494      6
7         23389     509      6
391       22401     509      6
452       23381     509      6
640       22091     509      6
763       22409     509      6
1029      22099     509      6
3003      22141     510      4
3697      22159     510      4
3846      23011     510      4
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482       22479     511      6
2000      22181     511      6
2648      22609     511      6
3644      22189     511      6
3790      22179     511      6
3957      22171     511      6
86        27301     512     17
141       27409     512     17
240       27419     512     17
270       22359     512     17
280       22369     512     17
805       27369     512     17
1914      27411     512     17
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3631      27329     512     17
3729      27429     512     17
4011      27309     512     17
4171      27421     512     17
4531      27351     512     17
4749      27359     512     17
5005      22351     512     17
806       27171     513      5
952       27169     513      5
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369       31039     514      4
499       31041     514      4
2576      31031     514      4
4106      31049     514      4
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478       31089     515      6
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1958      31201     515      6
3934      31061     515      6
4731      31071     515      6
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3798      23461     530      3
394       22399     531      6
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3004      22149     531      6
3616      22059     531      6
4451      22391     531      6
5132      22051     531      6
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1744      23501     532      7
1956      22229     532      7
3497      22169     532      7
3641      22161     532      7
3992      22221     532      7
522       22451     533     16
662       22459     533     16
1438      22231     533     16
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2389      22521     533     16
2507      22469     533     16
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4502      22511     533     16
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4781      22241     533     16
4866      22519     533     16
4867      22539     533     16
5003      22541     533     16
234       27431     534     12
246       27449     534     12
274       27391     534     12
339       27379     534     12
900       27371     534     12
1326      27439     534     12
1327      27441     534     12
1718      27381     534     12
2232      27389     534     12
3834      27341     534     12
4419      27399     534     12
4722      27349     534     12
558       31169     536      4
2495      31069     536      4
2683      31151     536      4
2848      31159     536      4
1223      32109     537      5
1569      32101     537      5
2627      31211     537      5
4812      34109     537      5
4813      34101     537      5
1110      32119     538      2
1587      32111     538      2
1196      32051     539      3
2140      32069     539      3
3682      32059     539      3
1614      22421     551      4
2249      22081     551      4
2659      22089     551      4
4538      22429     551      4
3354      22031     552      3
3971      22029     552      3
5124      22021     552      3
966       22289     553      8
1650      22559     553      8
2139      22309     553      8
3787      22191     553      8
3883      22199     553      8
3887      22299     553      8
4232      22271     553      8
5034      22551     553      8
151       22259     554     11
409       22449     554     11
986       22411     554     11
1220      22341     554     11
1432      22419     554     11
2122      22441     554     11
3511      27331     554     11
4625      22599     554     11
4974      22349     554     11
5049      22251     554     11
5140      22591     554     11
787       27109     555      2
3509      27101     555      2
1380      32049     559      4
1968      32039     559      4
2494      32041     559      4
3775      32031     559      4
2         32071     560      5
1136      32081     560      5
1476      32061     560      5
1684      32079     560      5
2589      32089     560      5
5069      33031     561      1
1711      22331     572      1
1         22069     573      5
333       22041     573      5
682       22079     573      5
799       22061     573      5
2287      22071     573      5
208       22281     574      2
691       22219     574      2
397       22509     575     10
501       22501     575     10
743       22491     575     10
1996      22579     575     10
2092      22501     575     10
2253      22009     575     10
3015      22561     575     10
3927      22499     575     10
4490      22569     575     10
5151      22571     575     10
677       27091     576      7
812       27459     576      7
890       27479     576      7
1852      27099     576      7
1950      27451     576      7
3468      27461     576      7
3469      27469     576      7
228       31171     578      3
656       31179     578      3
1001      31161     578      3
282       33029     582      5
1431      33019     582      5
2503      33039     582      5
4985      33021     582      5
5077      33011     582      5
596       34019     583      4
1153      33059     583      4
1384      34011     583      4
1930      33051     583      4
1254      34051     584      3
2336      34059     584      3
3010      34009     584      3
464       21099     593      1
692       21301     594      5
809       22019     594      5
1319      21311     594      5
1666      21309     594      5
2011      22011     594      5
297       21331     595     14
1567      21349     595     14
1720      21341     595     14
2082      21339     595     14
2353      21509     595     14
2457      22329     595     14
3289      21511     595     14
3290      21519     595     14
3488      22439     595     14
3543      21261     595     14
3643      22319     595     14
3909      21501     595     14
3967      21269     595     14
4525      22431     595     14
263       21369     596     10
323       21379     596     10
341       21399     596     10
500       21391     596     10
676       21371     596     10
1117      22481     596     10
1286      21411     596     10
1685      21419     596     10
2203      21361     596     10
4788      22489     596     10
123       27471     597      1
1037      33049     603      2
1244      33041     603      2
1560      34039     604      6
2393      34041     604      6
2546      34049     604      6
3893      34021     604      6
4344      34031     604      6
4361      34029     604      6
1752      21119     615      5
1901      21129     615      5
2213      21291     615      5
2451      21299     615      5
4971      21111     615      5
82        21319     616      7
2841      21489     616      7
3891      21329     616      7
4210      21481     616      7
4233      21321     616      7
4257      21499     616      7
4922      21491     616      7
418       21351     617      5
850       21259     617      5
1920      21691     617      5
4242      21359     617      5
4703      21251     617      5
72        21421     618     11
239       21431     618     11
936       21439     618     11
1046      21381     618     11
1899      21249     618     11
3229      21241     618     11
3456      21161     618     11
3457      21169     618     11
4056      21389     618     11
4384      21429     618     11
4955      21719     618     11
1015      30019     620      4
1425      30011     620      4
4005      31191     620      4
4739      31199     620      4
248       21531     637      4
330       21521     637      4
3270      21529     637      4
3695      21539     637      4
706       21451     638     12
1034      21449     638     12
1193      21711     638     12
1482      21409     638     12
1639      21689     638     12
1857      21459     638     12
1861      21441     638     12
2075      21681     638     12
2398      21239     638     12
4861      21231     638     12
4948      21229     638     12
4951      21699     638     12
564       21139     657      7
599       21149     657      7
623       21141     657      7
1625      21131     657      7
1787      21151     657      7
2225      21069     657      7
3395      21121     657      7
346       21559     658      9
415       21469     658      9
1156      21029     658      9
1165      21479     658      9
1378      21171     658      9
2840      21461     658      9
4094      21551     658      9
4441      21179     658      9
4506      21471     658      9
192       21611     659     10
197       21211     659     10
713       21609     659     10
846       21201     659     10
856       21279     659     10
1151      21209     659     10
2117      21601     659     10
3340      21271     659     10
3795      21219     659     10
4545      21619     659     10
9         28531     660     11
81        28521     660     11
1016      28409     660     11
1305      28391     660     11
1677      28401     660     11
1749      28399     660     11
2012      28529     660     11
2377      28541     660     11
4260      28611     660     11
4764      28411     660     11
5063      28539     660     11
725       30029     662      4
2317      30039     662      4
4029      30031     662      4
4385      30021     662      4
1838      21109     677      2
4040      21089     677      2
3717      21159     678      3
4064      21049     678      3
4065      21041     678      3
484       21541     679     17
539       21591     679     17
636       21181     679     17
1772      21191     679     17
1773      21199     679     17
1815      21581     679     17
2613      21571     679     17
3565      21751     679     17
3584      21589     679     17
3813      21189     679     17
3885      21639     679     17
4183      21599     679     17
4227      21549     679     17
4241      21631     679     17
4412      21579     679     17
4641      21759     679     17
4989      21561     679     17
353       28091     680      9
1611      28389     680      9
1683      28381     680      9
2502      21669     680      9
2753      28379     680      9
3387      28421     680      9
3524      21661     680      9
3630      28371     680      9
4805      28099     680      9
68        28161     681      6
757       28151     681      6
1186      28561     681      6
3598      28551     681      6
3738      28169     681      6
4406      28159     681      6
388       21079     699      2
2442      21071     699      2
2155      21019     700      8
2226      21011     700      8
2426      21769     700      8
2480      21021     700      8
3478      21779     700      8
4434      21761     700      8
4988      21569     700      8
4993      21771     700      8
1125      21621     701      8
1632      21659     701      8
2252      21641     701      8
2364      21679     701      8
4002      21649     701      8
4143      21629     701      8
4275      21651     701      8
4348      21671     701      8
161       28501     702      8
198       28571     702      8
736       28581     702      8
917       28511     702      8
1292      28601     702      8
2073      28519     702      8
4737      28591     702      8
4844      28509     702      8
66        30059     704      4
1262      30051     704      4
2909      30041     704      4
2910      30049     704      4
303       28351     722      4
1641      28369     722      4
4292      28359     722      4
4593      28361     722      4
171       28141     723      4
408       28139     723      4
931       28149     723      4
1287      28131     723      4
4026      30091     725      2
4028      30099     725      2
41        49249     730      2
528       49239     730      2
688       29029     741      4
2017      29021     741      4
2727      21059     741      4
2728      21051     741      4
1138      28279     743      4
1504      28269     743      4
2313      28261     743      4
4256      28271     743      4
403       28129     744      6
437       28121     744      6
3597      28469     744      6
3802      28471     744      6
5000      28499     744      6
5076      28491     744      6
306       49209     752      2
2118      49229     752      2
106       29041     761      4
1392      29019     761      4
2583      29049     761      4
4103      29011     761      4
389       20129     762      6
454       29039     762      6
473       20121     762      6
1691      29031     762      6
3558      20249     762      6
3562      20241     762      6
574       28259     763      2
4858      28251     763      2
404       28281     764     12
412       28349     764     12
457       28461     764     12
579       28459     764     12
611       28341     764     12
1129      28451     764     12
1143      28291     764     12
1222      28331     764     12
1311      28339     764     12
1670      28481     764     12
2357      28289     764     12
4152      28299     764     12
3412      43759     765      2
4145      43751     765      2
909       44689     767      8
993       44509     767      8
1558      44071     767      8
2098      44079     767      8
2153      44629     767      8
2254      30081     767      8
4453      30089     767      8
4479      44621     767      8
2423      49211     772      3
4369      49199     772      3
4616      49219     772      3
1800      20081     784      3
1853      29159     784      3
4263      20089     784      3
200       28439     785     10
912       28441     785     10
1108      28311     785     10
1149      28081     785     10
1282      28319     785     10
1288      28449     785     10
1905      28071     785     10
3516      28079     785     10
4341      28431     785     10
5113      28089     785     10
601       43341     786     11
1054      43769     786     11
1226      43761     786     11
1448      28111     786     11
1835      28119     786     11
2778      43453     786     11
2779      43452     786     11
2900      40321     786     11
2901      40329     786     11
3895      43459     786     11
4130      43349     786     11
2129      43789     787      4
2340      43781     787      4
2961      43771     787      4
2962      43779     787      4
430       44589     788      7
433       44581     788      7
1337      44559     788      7
2830      30119     788      7
2834      30109     788      7
2835      30101     788      7
3873      44551     788      7
163       44499     789      2
1946      44491     789      2
534       29129     803      2
4920      29121     803      2
47        20251     804     12
580       20211     804     12
777       20169     804     12
872       20161     804     12
3210      20201     804     12
3670      20179     804     12
4219      20209     804     12
4236      20219     804     12
4276      20239     804     12
4705      20171     804     12
4899      20231     804     12
4957      20259     804     12
1389      28239     805      9
2076      28201     805      9
2686      28009     805      9
3030      28211     805      9
3183      28301     805      9
3843      28241     805      9
4721      28199     805      9
4860      28249     805      9
4954      28231     805      9
372       28621     806      7
1056      28629     806      7
2053      28329     806      7
3177      28321     806      7
3692      43351     806      7
4080      43359     806      7
4787      43361     806      7
681       40301     807     13
2836      40309     807     13
2888      40351     807     13
2889      40359     807     13
2890      40311     807     13
2898      40341     807     13
2899      40349     807     13
2904      40339     807     13
3094      40361     807     13
3203      40369     807     13
4076      40379     807     13
4077      40371     807     13
5060      40331     807     13
416       43671     808      2
460       43679     808      2
214       44091     809     19
295       44501     809     19
612       44081     809     19
731       44089     809     19
1303      44511     809     19
1531      44579     809     19
2138      44459     809     19
2144      44451     809     19
2905      44591     809     19
2906      44599     809     19
3060      45451     809     19
3166      44529     809     19
3388      44519     809     19
3612      44569     809     19
4192      44469     809     19
4251      44461     809     19
4310      44571     809     19
4436      44521     809     19
4685      44561     809     19
1348      45249     810     10
1547      45299     810     10
1795      45259     810     10
2022      45291     810     10
2135      45311     810     10
2435      45319     810     10
2461      45241     810     10
2813      45461     810     10
2850      45469     810     10
3610      45251     810     10
138       49149     814      2
2469      49141     814      2
1452      46239     819      1
1356      29069     824      6
1428      29051     824      6
3481      29119     824      6
3907      29149     824      6
3995      29059     824      6
4115      29111     824      6
165       28221     826      6
298       20061     826      6
718       20069     826      6
3174      28309     826      6
3181      20271     826      6
3529      28229     826      6
139       28631     827      6
147       28061     827      6
641       28639     827      6
1275      28069     827      6
2241      28649     827      6
5056      28641     827      6
292       43531     828     13
335       43379     828     13
1910      43401     828     13
2240      43331     828     13
2902      43339     828     13
3672      43539     828     13
3709      43329     828     13
4081      43369     828     13
4093      43371     828     13
4120      43391     828     13
4137      43399     828     13
4467      43409     828     13
5161      43321     828     13
432       43681     829      6
1333      43481     829      6
1717      43841     829      6
2214      43489     829      6
2338      43499     829      6
2489      43491     829      6
2831      30111     830      7
2832      30129     830      7
2833      30121     830      7
3370      44181     830      7
3372      44189     830      7
5116      44879     830      7
5117      44871     830      7
1100      45239     831     10
1325      44399     831     10
3017      44009     831     10
3324      44481     831     10
3333      44539     831     10
3334      44541     831     10
3335      44489     831     10
3718      44549     831     10
4360      45231     831     10
4799      44531     831     10
364       45329     832     11
655       45321     832     11
2851      45341     832     11
3118      45349     832     11
3119      45331     832     11
3120      45339     832     11
3127      45261     832     11
3128      45271     832     11
3747      45269     832     11
4319      45479     832     11
4653      45279     832     11
619       49089     835      6
1601      49079     835      6
1770      45449     835      6
1881      45441     835      6
2526      49071     835      6
4382      49081     835      6
1860      29101     844      2
3874      29109     844      2
715       20189     846     12
1702      20159     846     12
2411      20151     846     12
2498      20191     846     12
2933      20149     846     12
2934      20141     846     12
3556      20059     846     12
3978      20051     846     12
4515      20261     846     12
4523      20269     846     12
4777      20199     846     12
4933      20181     846     12
1003      28051     847      6
2911      28041     847      6
2912      28049     847      6
2913      28059     847      6
3723      28651     847      6
3801      28659     847      6
183       43591     848      8
385       43511     848      8
1268      43519     848      8
1351      43389     848      8
1386      43691     848      8
2530      43699     848      8
3222      43381     848      8
4088      43599     848      8
700       43609     849      8
702       43601     849      8
705       43809     849      8
2875      43471     849      8
2876      43469     849      8
2877      43461     849      8
2878      43479     849      8
3782      43801     849      8
17        43659     850     12
124       43831     850     12
1415      43649     850     12
1583      43521     850     12
2221      43839     850     12
2598      43529     850     12
3520      43641     850     12
3633      44171     850     12
3634      44161     850     12
3635      44169     850     12
3875      43669     850     12
4009      44179     850     12
235       44441     851     14
450       44129     851     14
987       44111     851     14
1379      44291     851     14
1810      44121     851     14
1827      44101     851     14
2903      44881     851     14
3327      44479     851     14
3698      44119     851     14
3998      44449     851     14
4408      44391     851     14
4527      44109     851     14
5107      44471     851     14
5118      44889     851     14
1776      45309     852      4
1951      45301     852      4
4485      45361     852      4
4894      45369     852      4
526       45391     853     12
1370      45411     853     12
3122      45399     853     12
3684      45439     853     12
4016      45429     853     12
4020      45409     853     12
4053      45389     853     12
4308      45419     853     12
4329      45421     853     12
4607      45381     853     12
4690      45431     853     12
5008      45401     853     12
1127      49021     854      4
1199      49031     854      4
1421      49029     854      4
1562      49039     854      4
1167      49069     855      3
1420      49059     855      3
1841      49061     855      3
144       49169     856      3
1044      49151     856      3
2464      49159     856      3
242       29089     866      6
847       29081     866      6
1170      29071     866      6
1318      29091     866      6
2434      29139     866      6
2492      29099     866      6
342       20319     867      8
493       20341     867      8
945       20329     867      8
2425      20331     867      8
2915      20281     867      8
2922      20289     867      8
2957      20139     867      8
2958      20131     867      8
1626      28039     868      4
2979      28029     868      4
3791      28031     868      4
3886      28021     868      4
1479      28661     869      6
1580      28671     869      6
2649      28689     869      6
4154      28679     869      6
4532      28681     869      6
4950      28669     869      6
1465      43171     870     12
1609      43709     870     12
2625      43179     870     12
3103      43749     870     12
3104      43741     870     12
3105      43411     870     12
3109      43421     870     12
3410      43701     870     12
3411      43709     870     12
3983      43009     870     12
4190      43429     870     12
4774      43419     870     12
684       43571     871      4
708       43579     871      4
710       43589     871      4
714       43581     871      4
996       44151     872      4
1514      44159     872      4
5114      44899     872      4
5115      44891     872      4
2296      44299     873      1
2797      45049     874      9
2798      45031     874      9
2799      45039     874      9
2800      45379     874      9
2801      45371     874      9
2812      45489     874      9
2892      45491     874      9
3121      45351     874      9
3123      45359     874      9
1126      49019     875      4
1367      49011     875      4
2168      49139     875      4
4909      49131     875      4
59        45101     876      4
1052      49049     876      4
1150      49041     876      4
1987      49051     876      4
1437      49171     877      3
1918      49179     877      3
4938      49111     877      3
2916      17339     887      4
2917      17331     887      4
3808      20309     887      4
4370      20291     887      4
3515      20039     888      2
4133      20031     888      2
3486      28709     889      3
3547      28181     889      3
4946      28701     889      3
146       43611     890     12
396       43739     890     12
671       43509     890     12
822       43219     890     12
1203      43211     890     12
1724      43619     890     12
2855      43501     890     12
3227      43181     890     12
3350      43731     890     12
3351      43141     890     12
3352      43149     890     12
4695      43189     890     12
693       43561     891      4
1575      43569     891      4
3194      43541     891      4
3208      43549     891      4
343       44131     893     11
610       44271     893     11
947       44421     893     11
1873      44139     893     11
2267      44281     893     11
2321      44149     893     11
2399      44439     893     11
4246      44411     893     11
4645      44289     893     11
4743      44279     893     11
4846      44141     893     11
2802      45021     894      6
2803      45029     894      6
2804      45011     894      6
2805      44061     894      6
2806      45019     894      6
2891      44999     894      6
606       45171     895      9
648       45159     895      9
2054      45179     895      9
2473      45161     895      9
2795      45059     895      9
2796      45041     895      9
2811      45051     895      9
4940      45169     895      9
5033      45151     895      9
1358      45109     896      4
1395      45099     896      4
1727      45221     896      4
1813      45091     896      4
944       45149     897      6
1134      45121     897      6
1324      45141     897      6
2219      49109     897      6
2816      49091     897      6
2817      49099     897      6
1247      49121     898      4
1339      49129     898      4
2210      49181     898      4
4258      49189     898      4
2443      17311     908      4
2918      17329     908      4
2919      17321     908      4
2921      17319     908      4
468       20011     909      6
2235      20019     909      6
3182      20021     909      6
3620      20029     909      6
4141      17059     909      6
4328      20299     909      6
1688      28019     910      3
4194      28189     910      3
4202      28011     910      3
111       43311     911      7
638       43621     911      7
1317      43319     911      7
1513      28699     911      7
3490      42319     911      7
4519      42311     911      7
4952      28691     911      7
319       43439     912     10
631       43431     912     10
901       43449     912     10
1390      43169     912     10
1991      43191     912     10
2322      43229     912     10
2483      43221     912     10
3447      43199     912     10
4367      43161     912     10
5109      43441     912     10
1355      44051     915     12
1357      44791     915     12
2311      44861     915     12
2312      44799     915     12
2780      43991     915     12
3236      44811     915     12
3591      44069     915     12
4466      44059     915     12
4539      44801     915     12
4848      44869     915     12
4945      44809     915     12
5152      44819     915     12
605       45229     917      5
2807      45079     917      5
2808      45071     917      5
2809      45061     917      5
2810      45069     917      5
765       45111     918      3
1737      45129     918      3
4718      45119     918      3
2078      46031     919      4
2081      46039     919      4
3897      49119     919      4
4897      49101     919      4
1158      17361     928      4
4211      17309     928      4
4495      17369     928      4
4513      17301     928      4
117       17269     929      7
190       17079     929      7
922       17071     929      7
982       17141     929      7
1682      17149     929      7
3896      17069     929      7
5155      17061     929      7
563       17051     930      7
683       20101     930      7
871       17371     930      7
998       17009     930      7
1304      20109     930      7
2028      17379     930      7
3407      17189     930      7
3939      28109     931      2
5047      28101     931      2
3211      43629     932      1
40        43301     933     10
219       43309     933     10
624       43289     933     10
1027      43231     933     10
1224      43239     933     10
1481      43249     933     10
2042      43259     933     10
2183      43251     933     10
2199      43241     933     10
2360      43291     933     10
658       43721     934      4
2263      43719     934      4
3658      43099     934      4
3659      43091     934      4
288       44401     935     18
618       44639     935     18
1130      44029     935     18
2020      44631     935     18
2077      44259     935     18
2094      44649     935     18
2556      44859     935     18
2679      44031     935     18
2691      44909     935     18
2849      45009     935     18
2974      44049     935     18
3539      44041     935     18
3793      44641     935     18
4283      44019     935     18
4327      44021     935     18
4565      44731     935     18
4566      44739     935     18
5079      44251     935     18
202       45181     938      2
4714      45189     938      2
2862      46029     939      4
2866      46021     939      4
2963      45131     939      4
2964      45139     939      4
466       46041     940      2
711       46049     940      2
548       47701     942      2
2109      46609     942      2
337       17011     949      7
1398      17019     949      7
1699      16081     949      7
2642      17351     949      7
3566      17291     949      7
5032      17299     949      7
5048      17359     949      7
26        17049     950      7
552       17039     950      7
1391      17041     950      7
1741      17289     950      7
2101      17279     950      7
4131      17031     950      7
4838      17081     950      7
2453      17181     951      6
2482      17239     951      6
2980      17179     951      6
3048      17171     951      6
3404      17169     951      6
3405      17161     951      6
837       17439     952      6
1019      17409     952      6
1469      12209     952      6
1615      17419     952      6
2308      12201     952      6
2579      17399     952      6
186       42229     953     12
266       42299     953     12
824       42241     953     12
1368      42209     953     12
1369      42201     953     12
2306      42249     953     12
3899      42291     953     12
4193      42211     953     12
4199      42219     953     12
4237      42221     953     12
4509      42309     953     12
4926      42301     953     12
1310      43201     954      4
3814      43639     954      4
4207      43631     954      4
4628      43209     954      4
600       43151     955     14
758       43268     955     14
853       43271     955     14
1166      43819     955     14
1865      43267     955     14
2212      43059     955     14
2675      43811     955     14
2777      42991     955     14
2886      43261     955     14
2966      43061     955     14
3176      43051     955     14
3657      43069     955     14
4910      43279     955     14
4959      43159     955     14
262       43121     956      6
1183      44011     956      6
1496      43129     956      6
3652      43119     956      6
3654      43111     956      6
3655      43109     956      6
109       44651     957     13
230       44671     957     13
1212      44669     957     13
1523      44661     957     13
1633      44679     957     13
1697      44659     957     13
3860      44831     957     13
3862      44729     957     13
3916      44829     957     13
3917      44821     957     13
4100      44721     957     13
4295      44619     957     13
4862      44611     957     13
1588      45209     959      4
2359      45199     959      4
3712      45201     959      4
4708      45191     959      4
2704      46381     961      2
2705      46389     961      2
3618      46101     962      1
379       17389     970     11
852       17021     970     11
913       16009     970     11
2269      17029     970     11
2335      16139     970     11
3281      16199     970     11
3283      16149     970     11
3284      16191     970     11
4135      16141     970     11
4462      16131     970     11
4840      17381     970     11
905       17139     971     11
1012      17091     971     11
1033      17131     971     11
1470      16891     971     11
2345      17159     971     11
2400      17191     971     11
2984      17259     971     11
2986      17251     971     11
4025      16991     971     11
4834      17099     971     11
4911      17151     971     11
1109      17219     972      9
2211      12119     972      9
2406      17201     972      9
3408      17229     972      9
3661      12061     972      9
3662      12069     972      9
4669      17221     972      9
4696      17111     972      9
5142      17211     972      9
4740      17429     973      1
256       42191     974      6
1763      42199     974      6
2432      42171     974      6
3545      42181     974      6
4524      42179     974      6
5129      42189     974      6
1921      43041     975      4
4569      43829     975      4
4570      43821     975      4
4571      43049     975      4
1352      43869     976      7
1779      43859     976      7
2051      43879     976      7
3653      43071     976      7
3656      43089     976      7
3660      43081     976      7
4083      43891     976      7
3         44331     977     17
365       44191     977     17
381       44219     977     17
660       44201     977     17
685       44211     977     17
1250      44341     977     17
1511      44241     977     17
1822      44321     977     17
1863      44239     977     17
2003      44609     977     17
2470      44231     977     17
2965      44339     977     17
3169      44249     977     17
3737      44601     977     17
3767      44199     977     17
4528      44349     977     17
4758      44209     977     17
1204      44699     978      4
3861      44839     978      4
4688      44701     978      4
4692      44709     978      4
2187      46059     982      5
3527      46051     982      5
3806      46091     982      5
3889      46501     982      5
4610      46509     982      5
1769      46109     983      1
2121      46211     984      2
5139      46219     984      2
42        16051     991      9
663       16061     991      9
690       16071     991      9
1880      16069     991      9
2405      16249     991      9
2620      16059     991      9
2669      16079     991      9
4537      16241     991      9
4750      16089     991      9
811       17129     992      6
1360      17121     992      6
1631      16169     992      6
1774      16151     992      6
2176      16161     992      6
3232      16159     992      6
673       17241     993      6
978       17249     993      6
3221      19049     993      6
3740      17101     993      6
3741      17119     993      6
3742      17109     993      6
406       12079     994      4
1114      12081     994      4
2352      12071     994      4
4287      12089     994      4
1943      42161     995      5
2114      42169     995      5
3496      42239     995      5
3498      42151     995      5
4117      42231     995      5
1849      43011     996      5
3541      43019     996      5
3964      42119     996      5
4572      43029     996      5
4573      43021     996      5
3016      43961     997      3
4082      43899     997      3
4084      43969     997      3
828       44221     998     10
1525      43139     998     10
1540      44379     998     10
1868      44389     998     10
1871      44269     998     10
2363      44371     998     10
2640      44381     998     10
3745      43131     998     10
4557      44229     998     10
4761      43889     998     10
726       44691     999      7
3858      44779     999      7
3859      44771     999      7
3863      44929     999      7
3864      44921     999      7
3865      44919     999      7
3866      44911     999      7
164       48011    1001      3
3690      48019    1001      3
3991      45211    1001      3
120       46529    1003      9
436       46499    1003      9
863       46379    1003      9
1422      46511    1003      9
1736      46521    1003      9
2089      46371    1003      9
2395      46591    1003      9
2506      46519    1003      9
3098      46491    1003      9
753       46119    1004     10
977       46169    1004     10
1178      46161    1004     10
1234      46159    1004     10
2706      46088    1004     10
3477      46069    1004     10
3599      46149    1004     10
4153      46141    1004     10
4849      46151    1004     10
4990      46111    1004     10
1948      16231    1011      2
2409      16239    1011      2
114       16171    1012      8
355       16181    1012      8
1168      18311    1012      8
1753      18319    1012      8
2356      16189    1012      8
3530      18329    1012      8
4250      18321    1012      8
5136      16179    1012      8
455       19061    1013      5
2091      19069    1013      5
3217      19041    1013      5
3548      19051    1013      5
4526      19059    1013      5
958       12041    1014      6
1508      12051    1014      6
2282      12049    1014      6
3739      12111    1014      6
4807      12169    1014      6
4817      12059    1014      6
1242      12101    1015      2
2193      12109    1015      2
2844      42111    1016      6
3437      42259    1016      6
3965      42159    1016      6
4079      42099    1016      6
4243      42109    1016      6
4520      42091    1016      6
207       44369    1018      4
1006      44359    1018      4
2044      44361    1018      4
5145      44351    1018      4
1281      44301    1019      4
3504      44261    1019      4
4111      44329    1019      4
4939      44311    1019      4
938       46369    1023      4
1617      45591    1023      4
1678      46361    1023      4
3330      45599    1023      4
19        46709    1024     12
128       46189    1024     12
361       46079    1024     12
384       46589    1024     12
1232      46201    1024     12
1672      46579    1024     12
1743      46581    1024     12
2422      46209    1024     12
3385      46571    1024     12
4278      46019    1024     12
4811      46011    1024     12
4854      46071    1024     12
3977      47019    1025      2
4220      47011    1025      2
264       16041    1033      6
1598      16039    1033      6
2676      16049    1033      6
3266      16101    1033      6
3765      16031    1033      6
3821      16109    1033      6
1175      16099    1034      5
1986      16091    1034      5
4197      19071    1034      5
4677      19079    1034      5
4835      19089    1034      5
80        12199    1035      7
620       12141    1035      7
1949      12189    1035      7
2717      19039    1035      7
2718      19031    1035      7
3809      12179    1035      7
4224      12211    1035      7
344       12099    1036      2
762       12091    1036      2
12        42089    1037      6
2471      42061    1037      6
2722      42079    1037      6
3480      42141    1037      6
4114      42149    1037      6
4212      42071    1037      6
363       48029    1043      4
1180      48111    1043      4
1834      48021    1043      4
3833      48119    1043      4
112       46549    1045     12
788       46531    1045     12
1944      46611    1045     12
2177      46539    1045     12
3384      46561    1045     12
3386      46569    1045     12
3685      46629    1045     12
4071      45581    1045     12
4072      45589    1045     12
4288      46621    1045     12
4553      46619    1045     12
4675      46541    1045     12
462       46139    1046     11
2133      46241    1046     11
2236      46181    1046     11
2661      46131    1046     11
2927      46319    1046     11
2928      46311    1046     11
3923      46249    1046     11
4522      46129    1046     11
4611      46171    1046     11
4856      46179    1046     11
4924      46121    1046     11
56        15109    1053     13
76        16121    1053     13
420       15119    1053     13
451       16011    1053     13
1177      16029    1053     13
2558      16119    1053     13
2674      16019    1053     13
2764      16111    1053     13
3607      15111    1053     13
4336      16021    1053     13
4413      15101    1053     13
4818      16229    1053     13
5013      16221    1053     13
368       18129    1054     10
990       18221    1054     10
992       18239    1054     10
1919      18301    1054     10
2532      18339    1054     10
3172      18309    1054     10
4033      18121    1054     10
4478      18331    1054     10
4859      18071    1054     10
5094      18079    1054     10
199       19029    1055      6
358       19021    1055      6
814       19091    1055      6
3247      19099    1055      6
3980      19011    1055      6
4060      19019    1055      6
1729      12039    1056      6
2128      12031    1056      6
3326      11299    1056      6
3406      12029    1056      6
4354      12151    1056      6
5051      12021    1056      6
1544      48031    1064      1
182       46299    1066      7
223       46191    1066      7
973       46551    1066      7
1703      46008    1066      7
2342      46559    1066      7
2644      46291    1066      7
4170      46199    1066      7
278       47201    1067      4
3974      47029    1067      4
4624      47201    1067      4
4832      47021    1067      4
425       15219    1074     10
864       16209    1074     10
1200      15079    1074     10
1274      15229    1074     10
2027      16211    1074     10
2430      16219    1074     10
2887      16201    1074     10
3373      15221    1074     10
3563      15071    1074     10
4733      15211    1074     10
1160      18251    1075     12
1225      18109    1075     12
1497      18269    1075     12
2162      15121    1075     12
2682      15189    1075     12
3153      18249    1075     12
3420      15181    1075     12
3421      18241    1075     12
3430      15139    1075     12
3518      15131    1075     12
4422      18101    1075     12
4755      15129    1075     12
2630      18119    1076      4
3117      18141    1076      4
3321      19081    1076      4
4975      18149    1076      4
118       11291    1077      8
741       12129    1077      8
2361      11281    1077      8
2647      12139    1077      8
3164      11289    1077      8
4510      12149    1077      8
5042      12121    1077      8
5054      12131    1077      8
3487      42049    1079      3
3788      42051    1079      3
4918      42059    1079      3
1313      48039    1085      1
145       46349    1087     10
830       46339    1087     10
1316      46331    1087     10
1754      46359    1087     10
1884      46341    1087     10
3006      46321    1087     10
3537      46221    1087     10
3538      46229    1087     10
3823      46351    1087     10
4784      46329    1087     10
14        46261    1088      5
2143      46269    1088      5
2938      46309    1088      5
3876      46301    1088      5
4543      46271    1088      5
4656      15201    1094      1
597       15099    1095      6
940       15091    1095      6
4019      18281    1095      6
4294      18279    1095      6
4401      18271    1095      6
4691      18289    1095      6
88        18099    1096     11
791       18081    1096     11
1993      18089    1096     11
2231      18159    1096     11
2449      18059    1096     11
3148      18021    1096     11
3348      18069    1096     11
3349      18061    1096     11
3841      18029    1096     11
4746      18151    1096     11
4995      18051    1096     11
779       11379    1097     11
2156      11191    1097     11
3124      11351    1097     11
3125      11199    1097     11
3126      11009    1097     11
3665      11009    1097     11
3839      11189    1097     11
4198      11369    1097     11
4222      11359    1097     11
4476      11181    1097     11
4929      11361    1097     11
1142      11329    1098      6
1279      11301    1098      6
1462      11321    1098      6
2134      11311    1098      6
2368      11309    1098      6
3445      11319    1098      6
60        42039    1099      5
976       42031    1099      5
1543      42029    1099      5
2664      42021    1099      5
4235      42041    1099      5
2771      48131    1105      1
4418      48041    1106      2
4529      48049    1106      2
71        58479    1107      4
1780      58439    1107      4
2787      46989    1107      4
4536      58449    1107      4
334       46649    1108     11
405       46661    1108     11
1902      46251    1108     11
2178      46009    1108     11
3007      46281    1108     11
3008      46289    1108     11
3734      46669    1108     11
4359      46641    1108     11
4782      46639    1108     11
4783      46631    1108     11
5141      46279    1108     11
351       47039    1109      2
2305      47031    1109      2
2285      15209    1116      3
2424      15191    1116      3
4390      15199    1116      3
1767      18041    1117      5
2633      18131    1117      5
3049      18211    1117      5
4067      18049    1117      5
4482      18261    1117      5
735       11171    1118      2
1410      18179    1118      2
1122      11271    1119      5
2166      11279    1119      5
2511      11259    1119      5
3522      11269    1119      5
3523      11261    1119      5
196       11349    1120      6
1207      11331    1120      6
1889      42139    1120      6
2310      11339    1120      6
4713      11341    1120      6
5018      42131    1120      6
331       46979    1129     13
1557      47509    1129     13
1839      46969    1129     13
2058      46659    1129     13
2173      47579    1129     13
2401      47581    1129     13
2658      46651    1129     13
3733      46961    1129     13
4001      47589    1129     13
4706      46971    1129     13
5098      58461    1129     13
5102      47501    1129     13
5144      46951    1129     13
20        46831    1130     12
204       46451    1130     12
370       46449    1130     12
2318      46431    1130     12
2472      46459    1130     12
2618      46411    1130     12
3188      46441    1130     12
3759      46461    1130     12
4280      46421    1130     12
4736      46429    1130     12
4934      46439    1130     12
4969      46419    1130     12
637       47051    1131      4
1009      47041    1131      4
2638      47049    1131      4
3810      47059    1131      4
318       15159    1136      4
1161      15151    1136      4
3417      15169    1136      4
3435      15161    1136      4
696       18209    1138      9
1255      18171    1138      9
1731      18199    1138      9
1895      18189    1138      9
2791      18201    1138      9
3715      11449    1138      9
3766      11441    1138      9
4364      18181    1138      9
4900      18191    1138      9
2501      11179    1139      6
3115      11381    1139      6
3116      11409    1139      6
3272      11389    1139      6
3902      11401    1139      6
3969      11419    1139      6
899       42129    1141      4
4663      42011    1141      4
4664      42019    1141      4
4665      41081    1141      4
1922      48059    1148      2
4893      48051    1148      2
1347      46999    1149      3
2786      46981    1149      3
4400      46991    1149      3
257       46689    1150     14
810       46391    1150     14
1076      46401    1150     14
1373      46399    1150     14
1443      46769    1150     14
1456      46851    1150     14
1846      46681    1150     14
2549      46679    1150     14
2563      46699    1150     14
2914      46859    1150     14
3623      46671    1150     14
4454      46761    1150     14
4694      46691    1150     14
5143      46409    1150     14
2814      46479    1151      3
2815      46471    1151      3
3824      46469    1151      3
2518      14419    1157      1
1063      18011    1158      2
1894      18019    1158      2
5         11561    1159      6
486       11021    1159      6
1817      11609    1159      6
2268      11029    1159      6
3929      11039    1159      6
4279      11031    1159      6
543       11459    1160      9
889       11161    1160      9
910       11469    1160      9
1520      11061    1160      9
3606      11169    1160      9
3778      11069    1160      9
4340      11439    1160      9
4415      11429    1160      9
4614      11451    1160      9
99        47551    1171     12
421       47571    1171     12
1554      47499    1171     12
1555      47491    1171     12
1584      47521    1171     12
1595      47529    1171     12
1603      47539    1171     12
2158      47569    1171     12
2354      46869    1171     12
4006      47561    1171     12
4087      46861    1171     12
4166      47511    1171     12
97        46809    1172     12
176       46791    1172     12
544       46801    1172     12
669       46799    1172     12
1030      46811    1172     12
1900      46779    1172     12
2104      46841    1172     12
2191      46821    1172     12
4148      46781    1172     12
4312      47661    1172     12
4786      46789    1172     12
4937      46771    1172     12
424       47069    1173      6
1066      47071    1173      6
3383      46711    1173      6
3418      46719    1173      6
3500      47179    1173      6
4253      47061    1173      6
4514      47131    1174      1
91        15051    1178      9
95        15041    1178      9
96        15049    1178      9
285       15149    1178      9
2220      14401    1178      9
2281      15141    1178      9
2528      14189    1178      9
3898      14409    1178      9
3926      15059    1178      9
513       11511    1179      3
1068      11519    1179      3
3213      11019    1179      3
491       11159    1180     13
1053      11141    1180     13
1473      11151    1180     13
3151      11059    1180     13
3376      11489    1180     13
3379      11471    1180     13
4090      11599    1180     13
4132      11051    1180     13
4206      11149    1180     13
4544      11481    1180     13
4638      11479    1180     13
4719      11041    1180     13
5026      11049    1180     13
243       11221    1181      8
885       11079    1181      8
1023      11081    1181      8
1372      11071    1181      8
1936      11089    1181      8
2083      11229    1181      8
3424      11231    1181      8
4264      11239    1181      8
1401      41071    1183      3
2344      41089    1183      3
3167      41079    1183      3
3546      48061    1190      3
3812      48069    1190      3
4960      48079    1190      3
1174      47549    1192     11
2152      47559    1192     11
2720      47759    1192     11
2788      47751    1192     11
3356      47599    1192     11
3357      47641    1192     11
4323      47649    1192     11
4654      47541    1192     11
4775      47591    1192     11
4839      46871    1192     11
5015      46879    1192     11
2149      46731    1193      9
2229      46739    1193      9
2234      47671    1193      9
2247      46941    1193      9
2307      46489    1193      9
3555      46481    1193      9
4508      46881    1193      9
4831      46729    1193      9
4927      46721    1193      9
439       47079    1194     10
1013      47821    1194     10
1701      47089    1194     10
2204      47081    1194     10
3161      47189    1194     10
3239      47121    1194     10
3258      47129    1194     10
3642      47199    1194     10
3817      47169    1194     10
4505      47099    1194     10
2677      14429    1199      1
907       14369    1200      7
1173      14471    1200      7
2378      14399    1200      7
2702      14219    1200      7
2703      14501    1200      7
4399      14391    1200      7
4734      14211    1200      7
119       11531    1201     10
167       11131    1201     10
861       11521    1201     10
1302      11579    1201     10
1796      11539    1201     10
2023      11589    1201     10
2599      11139    1201     10
2639      11529    1201     10
4983      11541    1201     10
4984      11551    1201     10
49        11101    1203      5
426       11119    1203      5
3501      11099    1203      5
4712      11091    1203      5
5106      11109    1203      5
960       41069    1204      3
2575      41061    1204      3
4030      41051    1204      3
3569      48071    1211      1
102       46749    1214      9
505       46741    1214      9
703       47611    1214      9
1400      47609    1214      9
2111      47601    1214      9
2657      47619    1214      9
3722      47659    1214      9
3724      47651    1214      9
4322      47681    1214      9
2491      46931    1215      1
609       47091    1216      5
2493      47151    1216      5
3549      47109    1216      5
3966      47101    1216      5
4223      47141    1216      5
668       14171    1220     11
894       14329    1220     11
1231      14179    1220     11
1613      14509    1220     11
1798      14169    1220     11
1893      14161    1220     11
3367      14499    1220     11
3369      14359    1220     11
3378      14351    1220     11
4096      14041    1220     11
4729      14491    1220     11
302       10119    1221     10
802       10441    1221     10
866       10131    1221     10
1090      14209    1221     10
1455      10139    1221     10
1649      14201    1221     10
2510      10111    1221     10
3451      10599    1221     10
4487      10409    1221     10
5035      10449    1221     10
1121      11499    1222      6
1521      11491    1222      6
1828      10309    1222      6
4597      10301    1222      6
4824      10469    1222      6
4956      10461    1222      6
1042      11211    1223      4
1840      11201    1223      4
2420      11219    1223      4
4796      11209    1223      4
268       41109    1224      5
665       41119    1224      5
1903      11111    1224      5
1942      41101    1224      5
3252      41111    1224      5
1627      48089    1231      4
1926      48081    1231      4
3999      48091    1231      4
4852      48099    1231      4
3645      48149    1232      2
3786      48141    1232      2
1599      46911    1235      5
1630      46901    1235      5
1940      47629    1235      5
3180      47621    1235      5
3499      46891    1235      5
201       47819    1236      4
1818      47829    1236      4
2519      47811    1236      4
3492      58369    1236      4
795       14159    1241      2
1411      14151    1241      2
150       14199    1242      6
1802      14349    1242      6
3559      14191    1242      6
3743      14339    1242      6
3744      14331    1242      6
4403      14341    1242      6
84        10289    1243     12
132       10419    1243     12
142       10401    1243     12
807       10319    1243     12
920       10281    1243     12
991       10211    1243     12
1097      10411    1243     12
1681      10219    1243     12
2043      10291    1243     12
3133      10429    1243     12
4457      10299    1243     12
5159      10421    1243     12
327       41129    1246      5
1315      41041    1246      5
1407      41049    1246      5
2591      41121    1246      5
4078      41031    1246      5
3455      58289    1256      4
4151      58301    1256      4
4448      58271    1256      4
5075      58309    1256      4
1298      58351    1257      4
1648      46921    1257      4
2631      58359    1257      4
4962      58419    1257      4
1176      47801    1258      4
1409      47119    1258      4
2277      47111    1258      4
2433      47809    1258      4
790       14059    1262      3
924       14051    1262      3
1529      14049    1262      3
73        10659    1263     12
1000      10451    1263     12
1258      10091    1263     12
1833      10101    1263     12
2090      10009    1263     12
2339      10439    1263     12
2497      10099    1263     12
3134      10431    1263     12
3141      10459    1263     12
3475      10481    1263     12
4105      10109    1263     12
4416      10651    1263     12
79        13031    1264      7
963       10311    1264      7
2407      10321    1264      7
3143      10329    1264      7
4282      13039    1264      7
4789      10479    1264      7
4949      10471    1264      7
979       13029    1265      3
1758      13021    1265      3
3461      13019    1265      3
1171      41029    1266      3
2671      41011    1266      3
3019      41021    1266      3
687       41131    1267      3
2010      41139    1267      3
2256      41141    1267      3
1751      56081    1272      2
3686      56089    1272      2
253       57149    1273      8
804       48109    1273      8
831       48101    1273      8
3394      57011    1273      8
3397      57019    1273      8
3993      57029    1273      8
4465      57021    1273      8
4477      57141    1273      8
902       58311    1277     15
995       58349    1277     15
1349      58389    1277     15
1480      58329    1277     15
1705      58279    1277     15
2029      58421    1277     15
2288      58429    1277     15
2724      58319    1277     15
2726      58229    1277     15
2756      58221    1277     15
2758      58321    1277     15
2763      58259    1277     15
3254      58251    1277     15
3736      58341    1277     15
4379      58381    1277     15
876       58459    1278      5
2362      58451    1278      5
2615      58141    1278      5
3905      58361    1278      5
4267      58149    1278      5
1026      14009    1283      7
1433      14139    1283      7
1451      14129    1283      7
2137      14121    1283      7
3138      14119    1283      7
4358      14131    1283      7
5084      14141    1283      7
15        10339    1284      9
50        14281    1284      9
2159      14259    1284      9
2239      14279    1284      9
2601      14249    1284      9
3086      14269    1284      9
3453      10331    1284      9
3615      14271    1284      9
5133      14241    1284      9
492       10489    1285     11
659       10261    1285     11
1115      10181    1285     11
1276      10271    1285     11
2198      10269    1285     11
2619      10209    1285     11
2621      10189    1285     11
3139      10199    1285     11
3140      10201    1285     11
3142      10279    1285     11
4828      10191    1285     11
169       13041    1286      6
1785      13209    1286      6
3465      13011    1286      6
3669      09141    1286      6
3835      13049    1286      6
4699      13201    1286      6
255       41159    1289      4
2396      41149    1289      4
3872      41169    1289      4
4346      41151    1289      4
105       56061    1293      3
2136      56079    1293      3
2459      56071    1293      3
3393      56091    1294      2
3402      56099    1294      2
950       57049    1295      4
2170      57031    1295      4
3716      57039    1295      4
3961      57041    1295      4
279       58299    1298     10
1092      58399    1298     10
1217      58281    1298     10
2333      58391    1298     10
2653      58371    1298     10
2655      58379    1298     10
3260      58291    1298     10
3585      58571    1298     10
3588      58579    1298     10
4112      58241    1298     10
312       58121    1299      7
644       58129    1299      7
2026      58409    1299      7
2260      58131    1299      7
3594      58411    1299      7
4172      58139    1299      7
4635      58401    1299      7
999       14031    1304     12
1195      14319    1304     12
1674      14299    1304     12
1709      14379    1304     12
2116      14291    1304     12
2373      14021    1304     12
2666      14309    1304     12
3366      14381    1304     12
3696      14039    1304     12
4274      14029    1304     12
4468      14389    1304     12
4827      14489    1304     12
542       10341    1305     10
1608      10349    1305     10
1782      10171    1305     10
1824      10179    1305     10
2202      10089    1305     10
3209      10359    1305     10
3216      10351    1305     10
3997      10081    1305     10
4118      10379    1305     10
4435      10371    1305     10
4568      09149    1307      1
943       40231    1308      7
1024      41019    1308      7
2466      40091    1308      7
3458      40229    1308      7
3459      40081    1308      7
3463      40221    1308      7
4091      40099    1308      7
774       40259    1310      2
818       40251    1310      2
767       57051    1316      2
1866      57059    1316      2
1035      57071    1317      2
1541      57079    1317      2
540       57131    1318      2
752       57139    1318      2
64        58151    1319     16
137       58101    1319     16
1864      58331    1319     16
1887      58491    1319     16
1990      58211    1319     16
2041      58111    1319     16
2084      58009    1319     16
2297      58339    1319     16
2597      58481    1319     16
2757      58119    1319     16
3528      58489    1319     16
3710      58109    1319     16
4352      58499    1319     16
4380      58219    1319     16
4657      58159    1319     16
4727      58249    1319     16
1909      58171    1320      4
2227      58179    1320      4
4389      58161    1320      4
4420      58169    1320      4
1184      14519    1324      1
1099      14019    1325      5
1312      14101    1325      5
1989      14231    1325      5
2197      14109    1325      5
3694      14011    1325      5
546       10369    1326      6
1008      10071    1326      6
1426      10079    1326      6
1761      10501    1326      6
2175      10361    1326      6
2551      10061    1326      6
476       10231    1327      9
797       10239    1327      9
1493      10519    1327      9
1652      10241    1327      9
1746      10249    1327      9
2099      10381    1327      9
3189      10389    1327      9
4184      13051    1327      9
5134      13059    1327      9
287       09191    1328      9
593       13179    1328      9
893       09121    1328      9
1155      13181    1328      9
1467      09111    1328      9
3800      09159    1328      9
4552      09139    1328      9
4814      13189    1328      9
5137      09131    1328      9
964       40219    1329      4
2611      40211    1329      4
4195      40209    1329      4
4917      40201    1329      4
3460      40239    1330      2
4449      40249    1330      2
212       40261    1331      2
3984      40269    1331      2
352       53079    1333      4
380       53089    1333      4
1014      53081    1333      4
4757      53071    1333      4
2715      56029    1334      2
5160      56021    1334      2
1206      56059    1335      3
1645      56069    1335      3
3704      56051    1335      3
1340      55281    1336      2
3779      55289    1336      2
4043      59021    1337      2
4342      59029    1337      2
523       57061    1338      2
657       57069    1338      2
322       57111    1339      7
1221      57129    1339      7
1293      59139    1339      7
1363      59111    1339      7
2125      57119    1339      7
2179      59119    1339      7
2292      57121    1339      7
44        58019    1340      7
148       58039    1340      7
149       58031    1340      7
338       58031    1340      7
3851      58029    1340      7
3852      58021    1340      7
4179      58011    1340      7
630       58189    1341      1
972       14089    1346      7
1032      14239    1346      7
1144      14081    1346      7
1526      14229    1346      7
1600      10391    1346      7
3130      10399    1346      7
4550      14221    1346      7
1074      10161    1347      7
2314      10169    1347      7
2513      10141    1347      7
4265      10149    1347      7
4311      10121    1347      7
4987      10151    1347      7
4991      10129    1347      7
941       13121    1348     10
974       13139    1348     10
1300      13159    1348     10
1441      13171    1348     10
2049      13069    1348     10
2304      13062    1348     10
2315      13169    1348     10
3277      13079    1348     10
4486      13063    1348     10
4738      13141    1348     10
1093      09213    1349      4
1119      09169    1349      4
1885      09179    1349      4
2151      09212    1349      4
2523      40071    1350      4
2719      40079    1350      4
3464      40089    1350      4
4201      40119    1350      4
440       53061    1353      4
1252      53069    1353      4
3157      53059    1353      4
3158      53041    1353      4
313       53091    1354      6
1111      56269    1354      6
1572      56019    1354      6
1593      56261    1354      6
2716      56011    1354      6
5081      53099    1354      6
184       56039    1355      8
211       56041    1355      8
570       56191    1355      8
1673      56201    1355      8
2476      56209    1355      8
3764      56049    1355      8
3822      56031    1355      8
3850      56199    1355      8
1661      59011    1357      2
2033      59019    1357      2
2477      59031    1358      3
4351      59039    1358      3
4720      59041    1358      3
362       57081    1359     13
782       59309    1359     13
904       59559    1359     13
1651      59301    1359     13
1695      59089    1359     13
1859      59311    1359     13
2147      59081    1359     13
2650      59511    1359     13
2960      59319    1359     13
3091      59549    1359     13
3423      59541    1359     13
3826      57089    1359     13
4366      59551    1359     13
1486      59121    1360      8
1561      59129    1360      8
2584      59269    1360      8
3679      59261    1360      8
4032      59279    1360      8
4547      59271    1360      8
4615      59529    1360      8
4634      59521    1360      8
666       58049    1361     17
1458      58051    1361     17
2055      58041    1361     17
2417      58509    1361     17
2879      58519    1361     17
2880      58511    1361     17
2881      58529    1361     17
2882      58521    1361     17
2939      58261    1361     17
2940      58269    1361     17
3197      58501    1361     17
3204      58059    1361     17
3347      58069    1361     17
3365      58619    1361     17
3374      58601    1361     17
3377      58611    1361     17
4994      58609    1361     17
602       58191    1362      3
642       58199    1362      3
2261      58181    1362      3
581       10069    1368      5
1535      10051    1368      5
2690      10039    1368      5
2701      10499    1368      5
3985      10059    1368      5
832       06141    1369      8
1338      13119    1369      8
1457      06081    1369      8
2303      06131    1369      8
3705      06149    1369      8
4458      10229    1369      8
4842      06129    1369      8
5019      10221    1369      8
126       09011    1370      7
622       09022    1370      7
3462      13199    1370      7
3467      13191    1370      7
3958      09048    1370      7
3972      09047    1370      7
4428      09023    1370      7
2059      40051    1371      4
2894      40191    1371      4
2895      40199    1371      4
3603      40111    1371      4
187       51099    1372      2
3818      51091    1372      2
2347      51111    1373      2
4546      51119    1373      2
717       53039    1374      2
3224      53021    1374      2
1107      53361    1375      6
2592      53369    1375      6
3051      05349    1375      6
3057      53351    1375      6
3061      53359    1375      6
3070      53341    1375      6
1403      56241    1376      6
2185      56251    1376      6
4540      56289    1376      6
4710      56249    1376      6
5046      54161    1376      6
5147      54169    1376      6
882       55279    1378      2
3629      55271    1378      2
2695      59721    1379      2
2696      59729    1379      2
474       59321    1380     11
475       59561    1380     11
481       59329    1380     11
865       59051    1380     11
892       59049    1380     11
937       59331    1380     11
1519      59059    1380     11
1882      59339    1380     11
2444      59421    1380     11
2446      59429    1380     11
4769      59569    1380     11
948       59079    1381     10
2439      59131    1381     10
2460      59149    1381     10
3192      59159    1381     10
3193      59141    1381     10
3198      59091    1381     10
3199      59099    1381     10
4007      59109    1381     10
4008      59101    1381     10
4044      59072    1381     10
1581      58541    1382      5
1591      58549    1382      5
2883      58531    1382      5
2885      58539    1382      5
3368      58621    1382      5
156       58201    1383      5
2884      58061    1383      5
3605      58209    1383      5
3699      58071    1383      5
4121      58079    1383      5
1610      14061    1388      5
1620      14071    1388      5
3534      10049    1388      5
3535      10041    1388      5
5103      14069    1388      5
1272      06051    1389      5
1394      06031    1389      5
2542      06069    1389      5
4726      06071    1389      5
5041      06049    1389      5
77        09059    1390      6
244       13091    1390      6
1346      13099    1390      6
4262      13071    1390      6
4496      13081    1390      6
5067      13089    1390      6
1025      40171    1391      3
2529      09219    1391      3
3678      40179    1391      3
1038      40059    1392      2
4549      40069    1392      2
92        51029    1393      6
667       51049    1393      6
1330      51039    1393      6
1690      51041    1393      6
4430      51031    1393      6
4446      51021    1393      6
65        51069    1394      9
348       53019    1394      9
508       51131    1394      9
2050      53111    1394      9
3470      51071    1394      9
3471      51079    1394      9
3472      51071    1394      9
4698      53011    1394      9
4744      53119    1394      9
233       53189    1395      8
720       53291    1395      8
1843      53171    1395      8
2130      53181    1395      8
3155      53049    1395      8
3156      53041    1395      8
3159      53179    1395      8
4277      53199    1395      8
2478      54069    1396      8
4097      54211    1396      8
4119      54629    1396      8
4134      54621    1396      8
4159      54061    1396      8
4456      54219    1396      8
4997      54181    1396      8
4998      54189    1396      8
1533      55119    1397      9
1816      56259    1397      9
1844      55111    1397      9
1957      55121    1397      9
2069      55141    1397      9
3444      55011    1397      9
3450      55019    1397      9
4617      55129    1397      9
5074      55131    1397      9
33        55351    1398      8
517       55251    1398      8
646       55361    1398      8
1010      55259    1398      8
1344      55269    1398      8
1444      55371    1398      8
3842      55261    1398      8
4320      55381    1398      8
174       59441    1400      6
594       59449    1400      6
2512      59481    1400      6
2907      59509    1400      6
4751      59501    1400      6
4943      59499    1400      6
707       59061    1401     13
1235      59341    1401     13
2148      59361    1401     13
2394      59069    1401     13
2792      58991    1401     13
3185      59073    1401     13
3731      59691    1401     13
4015      59669    1401     13
4070      59671    1401     13
4317      59661    1401     13
4321      59699    1401     13
4815      59619    1401     13
4816      59611    1401     13
357       59251    1402      8
955       59221    1402      8
1698      59211    1402      8
1890      59231    1402      8
4488      59259    1402      8
5009      59229    1402      8
5017      59239    1402      8
5036      59219    1402      8
1253      58099    1404      4
1530      58089    1404      4
1665      58091    1404      4
1964      58081    1404      4
1459      10021    1410     13
1637      05521    1410     13
1933      10011    1410     13
2150      05241    1410     13
3099      06029    1410     13
3136      05259    1410     13
3154      10017    1410     13
3325      06011    1410     13
3328      05069    1410     13
3331      05012    1410     13
3338      05019    1410     13
3466      10018    1410     13
4176      05239    1410     13
839       06151    1411      7
965       13211    1411      7
1424      06039    1411      7
1999      06161    1411      7
2309      06169    1411      7
2566      06159    1411      7
3028      04321    1411      7
39        08137    1412      6
45        08111    1412      6
1251      09037    1412      6
2086      08138    1412      6
2374      09038    1412      6
3329      08121    1412      6
175       40031    1413     10
887       50069    1413     10
1436      40121    1413     10
2200      40129    1413     10
3399      50061    1413     10
3482      40189    1413     10
3803      40181    1413     10
3903      40041    1413     10
4684      40039    1413     10
4930      40049    1413     10
52        50059    1414      7
849       51101    1414      7
916       50051    1414      7
1532      51011    1414      7
2131      51109    1414      7
3836      51019    1414      7
5044      50041    1414      7
701       52249    1415     10
895       51059    1415     10
1062      51051    1415     10
3096      52211    1415     10
3380      51089    1415     10
3426      52219    1415     10
3429      52551    1415     10
3440      52559    1415     10
4469      51081    1415     10
4878      52241    1415     10
653       53139    1416      7
728       53299    1416      7
2673      53129    1416      7
3107      53319    1416      7
3225      53029    1416      7
4109      53131    1416      7
4357      53121    1416      7
347       53159    1417     13
554       53191    1417     13
836       53331    1417     13
2186      53339    1417     13
2331      53161    1417     13
2334      53201    1417     13
2467      53169    1417     13
4459      53209    1417     13
4658      54611    1417     13
4724      53329    1417     13
4725      53321    1417     13
4936      53151    1417     13
5020      54619    1417     13
62        54201    1418      6
557       54229    1418      6
2145      54209    1418      6
3144      54199    1418      6
3680      54221    1418      6
4999      54191    1418      6
180       55159    1419     11
613       55179    1419     11
1973      55331    1419     11
1982      55171    1419     11
2209      55021    1419     11
3446      55341    1419     11
3449      55349    1419     11
4168      55149    1419     11
4470      55029    1419     11
4551      55151    1419     11
4992      55339    1419     11
411       59299    1422     11
467       59379    1422     11
477       59439    1422     11
723       59349    1422     11
1145      59289    1422     11
1154      59291    1422     11
1643      59431    1422     11
1925      59369    1422     11
2095      59371    1422     11
3400      59711    1422     11
4362      59281    1422     11
178       59179    1423     11
446       59389    1423     11
675       59249    1423     11
862       59171    1423     11
1059      59351    1423     11
1551      59241    1423     11
2074      59381    1423     11
3195      59169    1423     11
3332      59161    1423     11
4031      59189    1423     11
5138      59181    1423     11
471       05519    1430     11
504       05629    1430     11
515       05641    1430     11
1106      05419    1430     11
1764      05411    1430     11
2699      03241    1430     11
3129      03222    1430     11
3531      05649    1430     11
3799      05651    1430     11
4069      05431    1430     11
4169      05631    1430     11
851       05059    1431     10
1045      06189    1431     10
1668      05023    1431     10
1669      05131    1431     10
2245      05049    1431     10
2246      05129    1431     10
3687      05039    1431     10
3884      06171    1431     10
4772      05013    1431     10
5082      05022    1431     10
435       08057    1432      7
1064      13101    1432      7
1197      13109    1432      7
2552      08019    1432      7
3794      08011    1432      7
4481      04311    1432      7
4676      08031    1432      7
3805      40021    1433      4
3962      40279    1433      4
4204      40271    1433      4
4919      40029    1433      4
1218      50049    1434      7
1260      50038    1434      7
1570      50111    1434      7
1994      50037    1434      7
4836      50119    1434      7
4864      50031    1434      7
5083      50021    1434      7
1322      52071    1435      4
1788      52079    1435      4
1842      52139    1435      4
4290      52131    1435      4
1897      51139    1436      4
3108      53311    1436      4
3273      52011    1436      4
3274      52019    1436      4
1377      53389    1437      4
1552      53141    1437      4
1877      53149    1437      4
4535      53381    1437      4
502       54011    1438      6
2431      54248    1438      6
2534      54231    1438      6
2708      54019    1438      6
3190      54241    1438      6
3986      54239    1438      6
51        55509    1439     14
858       55139    1439     14
1202      54259    1439     14
1334      55181    1439     14
2208      54459    1439     14
2454      54451    1439     14
2714      55209    1439     14
3074      54469    1439     14
3075      54461    1439     14
3087      55201    1439     14
3200      55199    1439     14
3207      55169    1439     14
3666      54051    1439     14
4095      55189    1439     14
592       55031    1440      6
877       55249    1440      6
1098      55229    1440      6
1539      55241    1440      6
1658      55039    1440      6
3235      55041    1440      6
2697      59741    1442      5
2767      59749    1442      5
2774      59731    1442      5
2775      59739    1442      5
2978      59719    1442      5
395       59411    1443     12
928       59409    1443     12
1002      59459    1443     12
1714      59639    1443     12
1829      59419    1443     12
2349      59359    1443     12
2634      59401    1443     12
3170      59631    1443     12
3727      59701    1443     12
4021      59709    1443     12
4281      59451    1443     12
4604      59651    1443     12
989       59201    1444      4
1192      59199    1444      4
3936      59191    1444      4
4809      59209    1444      4
533       03111    1452     10
1102      05421    1452     10
1619      03071    1452     10
2244      05429    1452     10
2414      03223    1452     10
3135      05271    1452     10
3137      05269    1452     10
3649      03129    1452     10
4110      03151    1452     10
4424      05189    1452     10
24        04149    1453     10
518       04251    1453     10
1984      04229    1453     10
2365      04223    1453     10
3029      04329    1453     10
3542      04339    1453     10
3848      04239    1453     10
3849      04222    1453     10
4302      04219    1453     10
4303      04211    1453     10
4414      07011    1454      2
4473      08058    1454      2
16        50011    1455      6
1263      50079    1455      6
1997      50029    1455      6
4228      50071    1455      6
4472      50019    1455      6
4707      50351    1455      6
393       50169    1456      8
1962      50171    1456      8
2036      50161    1456      8
2107      52471    1456      8
2337      50179    1456      8
3215      52479    1456      8
4326      50191    1456      8
4630      50189    1456      8
57        52141    1457     15
74        52149    1457     15
470       52271    1457     15
722       52159    1457     15
732       52199    1457     15
820       52201    1457     15
1216      52169    1457     15
1256      52229    1457     15
1374      52221    1457     15
1463      52191    1457     15
2561      52209    1457     15
4068      52151    1457     15
4410      52179    1457     15
4444      52161    1457     15
5050      52171    1457     15
177       53211    1458      9
304       53229    1458      9
340       53219    1458      9
1060      53009    1458      9
1353      53221    1458      9
3688      53231    1458      9
4259      53239    1458      9
4356      53309    1458      9
4371      53301    1458      9
1416      54081    1459      6
1998      54079    1459      6
3994      54089    1459      6
4061      54071    1459      6
4167      53371    1459      6
4612      53379    1459      6
98        54059    1460     10
160       54031    1460     10
1634      54039    1460     10
2262      54391    1460     10
2617      54041    1460     10
3069      54341    1460     10
4397      54049    1460     10
4404      54251    1460     10
4463      54349    1460     10
4771      54399    1460     10
32        55231    1461     10
399       55301    1461     10
536       55311    1461     10
541       55319    1461     10
567       55221    1461     10
724       55309    1461     10
1215      55239    1461     10
1528      55219    1461     10
1696      55009    1461     10
3913      55211    1461     10
1732      59461    1464     11
1836      59581    1464     11
2692      59471    1464     11
2693      59479    1464     11
2694      59589    1464     11
2765      59759    1464     11
2766      59751    1464     11
2776      59761    1464     11
3173      59579    1464     11
4330      59469    1464     11
4534      59571    1464     11
561       59399    1465      7
1049      59649    1465      7
1291      59391    1465      7
2783      59621    1465      7
3568      59809    1465      7
4017      59641    1465      7
4101      59801    1465      7
463       03239    1472      5
2284      03217    1472      5
2388      03219    1472      5
2484      03211    1472      5
4996      03218    1472      5
537       03021    1473      8
1011      05029    1473      8
1693      05319    1473      8
2376      05009    1473      8
2652      03031    1473      8
2854      03041    1473      8
4825      03019    1473      8
5029      05199    1473      8
87        01013    1474     16
459       01019    1474     16
704       04142    1474     16
975       04143    1474     16
1018      07509    1474     16
1159      04179    1474     16
1335      01012    1474     16
2018      04121    1474     16
2072      04029    1474     16
3567      08079    1474     16
3987      04159    1474     16
4438      04111    1474     16
4439      08041    1474     16
4583      04019    1474     16
4584      08069    1474     16
4701      04151    1474     16
2013      40019    1475      6
2490      40011    1475      6
3484      40101    1475      6
3816      40109    1475      6
4562      07031    1475      6
5078      07111    1475      6
535       50121    1476      4
2554      50129    1476      4
4672      50229    1476      4
4673      50221    1476      4
191       52269    1477     14
410       52251    1477     14
689       52501    1477     14
845       52261    1477     14
1307      52181    1477     14
1404      52509    1477     14
2174      52259    1477     14
2350      52321    1477     14
3276      52231    1477     14
3711      52329    1477     14
3748      52008    1477     14
3749      52009    1477     14
3797      52189    1477     14
4759      52239    1477     14
311       53409    1478      9
511       52029    1478      9
551       53401    1478      9
1553      52021    1478      9
1891      53419    1478      9
3291      52031    1478      9
3293      52449    1478      9
3297      52441    1478      9
4776      52039    1478      9
205       53391    1479      8
572       54531    1479      8
785       53269    1479      8
911       53261    1479      8
1086      53399    1479      8
2015      54539    1479      8
4129      53249    1479      8
4140      53241    1479      8
768       54247    1480      6
1616      54339    1480      6
2031      54331    1480      6
3476      54261    1480      6
3519      54269    1480      6
4426      54009    1480      6
1364      54351    1481      4
1538      55321    1481      4
1689      55329    1481      4
5072      54359    1481      4
3233      55049    1482      4
4058      55059    1482      4
4286      55051    1482      4
4986      55071    1482      4
294       59781    1485      9
1239      59591    1485      9
1995      59601    1485      9
2324      59599    1485      9
2448      59609    1485      9
2789      59771    1485      9
2818      59779    1485      9
3601      59811    1485      9
3726      59819    1485      9
760       03381    1494      5
764       03529    1494      5
879       03391    1494      5
2206      03059    1494      5
4010      03539    1494      5
545       02061    1495     10
608       02031    1495     10
1750      02119    1495     10
1854      04167    1495     10
2119      04168    1495     10
3271      02029    1495     10
4066      04249    1495     10
5091      02181    1495     10
5092      02111    1495     10
5093      02011    1495     10
293       01112    1496     14
1342      07589    1496     14
2021      07021    1496     14
2070      07529    1496     14
2272      07571    1496     14
2274      07518    1496     14
2276      07517    1496     14
2504      07551    1496     14
2874      07569    1496     14
2995      01113    1496     14
2996      01059    1496     14
3890      07539    1496     14
4521      07531    1496     14
5149      07561    1496     14
730       50301    1497      9
3259      07211    1497      9
3268      50321    1497      9
3970      50279    1497      9
4024      50251    1497      9
4086      50261    1497      9
4318      50259    1497      9
4678      50089    1497      9
4679      50081    1497      9
317       50211    1498     11
506       52411    1498     11
577       52409    1498     11
1397      52499    1498     11
1498      50159    1498     11
1654      50209    1498     11
1664      50201    1498     11
1858      52099    1498     11
2196      50199    1498     11
2387      52419    1498     11
3506      52401    1498     11
301       52439    1499     14
472       52281    1499     14
747       52289    1499     14
914       52291    1499     14
1518      52349    1499     14
1978      52341    1499     14
2259      52299    1499     14
3292      52369    1499     14
3298      52539    1499     14
3301      52361    1499     14
3304      52359    1499     14
3305      52351    1499     14
4542      52279    1499     14
4963      52371    1499     14
345       53289    1500      6
519       53271    1500      6
2080      53251    1500      6
2163      53259    1500      6
3510      53279    1500      6
4142      53281    1500      6
251       54321    1501     10
744       54099    1501     10
838       54091    1501     10
1057      54609    1501     10
2184      54319    1501     10
3286      54371    1501     10
3503      54379    1501     10
3918      54311    1501     10
4365      54329    1501     10
4857      54601    1501     10
8         54411    1502     12
321       54571    1502     12
556       54271    1502     12
808       54479    1502     12
942       54419    1502     12
1201      54409    1502     12
1328      54441    1502     12
1341      54471    1502     12
1427      54489    1502     12
1783      54449    1502     12
3196      54401    1502     12
4461      54579    1502     12
172       59789    1506      1
3131      03569    1514      3
3132      03561    1514      3
4036      03339    1514      3
817       03011    1515      1
289       01119    1516     18
427       01039    1516     18
559       01639    1516     18
898       01621    1516     18
953       02149    1516     18
1067      01629    1516     18
1082      02141    1516     18
1140      80159    1516     18
1213      80151    1516     18
1419      01139    1516     18
1781      01511    1516     18
2711      01611    1516     18
3371      01631    1516     18
3533      01619    1516     18
3924      01541    1516     18
4063      01029    1516     18
4741      02049    1516     18
4970      01519    1516     18
497       07231    1517      4
1687      07319    1517      4
4347      07331    1517      4
5108      07419    1517      4
284       50991    1518      7
962       50331    1518      7
1188      50239    1518      7
2604      50231    1518      7
3683      50249    1518      7
4405      50349    1518      7
4558      50241    1518      7
1091      52319    1519      6
2920      52309    1519      6
2923      52301    1519      6
2924      52339    1519      6
2925      52331    1519      6
5154      52311    1519      6
3294      52061    1520      5
3299      52529    1520      5
3300      52069    1520      5
3302      52051    1520      5
3303      52059    1520      5
367       54109    1521      3
3920      54101    1521      3
4261      54369    1521      3
841       54291    1522      8
1157      54281    1522      8
1602      54299    1522      8
3574      54581    1522      8
3921      54279    1522      8
4343      54381    1522      8
4556      54389    1522      8
4700      54289    1522      8
78        54481    1523      1
1039      55089    1524      5
3953      55109    1524      5
3954      55101    1524      5
4057      55079    1524      5
4394      55081    1524      5
3604      59791    1527      3
4297      68171    1527      3
4298      68179    1527      3
3915      03421    1535      1
4037      03331    1536      3
4822      03519    1536      3
4823      03511    1536      3
218       02151    1537      9
635       02171    1537      9
1139      02101    1537      9
1172      02169    1537      9
1259      02099    1537      9
1797      02161    1537      9
1912      02159    1537      9
2251      02089    1537      9
3847      02051    1537      9
116       01239    1538     15
603       01129    1538     15
868       01521    1538     15
881       01231    1538     15
956       01229    1538     15
1646      01121    1538     15
1757      01211    1538     15
2258      01549    1538     15
2286      80161    1538     15
2290      01529    1538     15
2948      01411    1538     15
3689      01419    1538     15
4254      01559    1538     15
4266      01109    1538     15
4876      01219    1538     15
870       07329    1539     12
1721      07241    1539     12
1961      07221    1539     12
2533      07249    1539     12
2700      07351    1539     12
2865      60019    1539     12
2867      07359    1539     12
2868      60011    1539     12
3401      60101    1539     12
3507      60099    1539     12
3956      07361    1539     12
4270      60191    1539     12
1343      52129    1540      7
2772      52049    1540      7
2773      52059    1540      7
3202      60241    1540      7
3829      52451    1540      7
5001      60251    1540      7
5153      52109    1540      7
25        52429    1541      7
261       52389    1541      7
401       52391    1541      7
586       52481    1541      7
1447      52399    1541      7
1979      52381    1541      7
2577      52489    1541      7
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2999      67641    1756     11
3000      67649    1756     11
4882      67419    1756     11
4883      67411    1756     11
4982      67429    1756     11
5053      67591    1756     11
5064      67599    1756     11
5095      67421    1756     11
3870      65449    1757      2
3871      65441    1757      2
213       91121    1768      4
305       91101    1768      4
918       91131    1768      4
3828      92261    1768      4
398       82121    1769      8
1446      82129    1769      8
1509      82089    1769      8
1512      82079    1769      8
1959      82071    1769      8
2456      82081    1769      8
3900      82131    1769      8
4000      82139    1769      8
2035      82221    1770      3
2505      82032    1770      3
4388      82033    1770      3
90        70071    1771     10
225       71149    1771     10
521       70079    1771     10
921       70089    1771     10
1375      71141    1771     10
1692      70081    1771     10
3031      70409    1771     10
3032      70401    1771     10
3784      71129    1771     10
4231      71121    1771     10
555       71049    1772      5
2643      71189    1772      5
4271      71041    1772      5
4517      71191    1772      5
5146      71181    1772      5
733       64239    1774      9
796       64041    1774      9
1185      64231    1774      9
1289      64049    1774      9
1550      64241    1774      9
2972      64301    1774      9
2973      64309    1774      9
4062      64019    1774      9
5016      64249    1774      9
104       64029    1775      8
756       65011    1775      8
1007      65019    1775      8
1730      64021    1775      8
3245      67719    1775      8
4498      67729    1775      8
4501      67711    1775      8
4693      67721    1775      8
159       67341    1776     14
857       67191    1776     14
1096      67189    1776     14
1867      67199    1776     14
2330      67241    1776     14
2421      67109    1776     14
2580      67009    1776     14
2949      67759    1776     14
3095      67181    1776     14
3912      67409    1776     14
3914      67401    1776     14
4338      67249    1776     14
4378      67101    1776     14
4381      67349    1776     14
1766      65149    1777     10
1771      65141    1777     10
2685      65499    1777     10
3005      65491    1777     10
3064      65339    1777     10
3065      65331    1777     10
3278      65439    1777     10
3856      65579    1777     10
3857      65571    1777     10
4680      65431    1777     10
2684      65451    1778      2
3592      65641    1778      2
36        82059    1790     10
1146      82051    1790     10
1792      92111    1790     10
2250      92101    1790     10
2654      92091    1790     10
3681      92119    1790     10
3840      92099    1790     10
4059      92249    1790     10
4349      92241    1790     10
4492      92109    1790     10
751       82221    1791      6
1065      82151    1791      6
3608      82229    1791      6
3675      82171    1791      6
4636      82049    1791      6
5021      82159    1791      6
70        71101    1792      6
224       71111    1792      6
4793      71119    1792      6
4798      71201    1792      6
4800      71209    1792      6
4801      71109    1792      6
237       71071    1793      4
951       71079    1793      4
3033      71331    1793      4
3034      71339    1793      4
1022      73041    1794      3
2440      73019    1794      3
3676      73049    1794      3
222       64221    1795      4
378       64229    1795      4
2298      64219    1795      4
4174      64131    1795      4
438       64059    1796     12
547       64069    1796     12
1506      64051    1796     12
1606      64079    1796     12
2004      64071    1796     12
2019      64319    1796     12
4013      62271    1796     12
4045      64321    1796     12
4587      62261    1796     12
4709      64329    1796     12
5006      64061    1796     12
5052      64311    1796     12
786       65021    1797     14
1266      67151    1797     14
1607      67141    1797     14
1734      67159    1797     14
1830      65031    1797     14
1935      67501    1797     14
2061      65039    1797     14
2372      67219    1797     14
2458      67179    1797     14
2588      65029    1797     14
3062      67161    1797     14
3364      67169    1797     14
3443      67211    1797     14
4247      67171    1797     14
578       67439    1798      6
2123      67251    1798      6
3409      67431    1798      6
3735      65061    1798      6
4051      65069    1798      6
4373      67259    1798      6
583       65601    1799     11
590       65609    1799     11
1229      65611    1799     11
1230      65619    1799     11
2937      65469    1799     11
3160      65671    1799     11
3163      65679    1799     11
3253      65461    1799     11
3339      65459    1799     11
4554      65409    1799     11
4689      65401    1799     11
4968      65651    1800      1
761       92129    1811      6
794       82141    1811      6
1187      92179    1811      6
2205      92171    1811      6
2320      82149    1811      6
4157      92121    1811      6
664       82009    1812      6
1028      83109    1812      6
4561      82061    1812      6
4563      83101    1812      6
4841      83119    1812      6
4873      82069    1812      6
387       71089    1813     10
1306      71099    1813     10
2842      71139    1813     10
3554      71131    1813     10
3880      72059    1813     10
4516      72051    1813     10
4564      71091    1813     10
4574      72029    1813     10
4581      72021    1813     10
4745      71081    1813     10
166       62251    1817      6
848       64409    1817      6
2237      62251    1817      6
4374      64401    1817      6
4429      67739    1817      6
4586      67731    1817      6
113       65059    1818     13
748       67121    1818     13
780       67119    1818     13
815       67139    1818     13
878       67129    1818     13
2273      67111    1818     13
2375      65049    1818     13
2408      65041    1818     13
2455      67231    1818     13
2509      67239    1818     13
3454      67671    1818     13
4124      67221    1818     13
4139      67229    1818     13
531       65219    1819     16
734       65251    1819     16
1277      65229    1819     16
1280      65221    1819     16
2863      65359    1819     16
2869      65351    1819     16
3175      65099    1819     16
3551      65209    1819     16
3751      65009    1819     16
3773      65089    1819     16
4160      65201    1819     16
4433      65259    1819     16
4494      65091    1819     16
4686      65341    1819     16
4687      65349    1819     16
4754      65081    1819     16
1233      65629    1820      3
1236      65621    1820      3
1238      65631    1820      3
217       92041    1832      7
524       92059    1832      7
582       92049    1832      7
1214      92251    1832      7
1850      92051    1832      7
2594      92189    1832      7
3275      92181    1832      7
31        83139    1833     13
185       83029    1833     13
527       83319    1833     13
1020      83299    1833     13
1430      83169    1833     13
1823      83149    1833     13
1967      83159    1833     13
2445      83291    1833     13
2499      83131    1833     13
4163      83151    1833     13
4284      82181    1833     13
5088      82179    1833     13
5104      83311    1833     13
1412      72011    1834      3
3147      72019    1834      3
5012      83111    1834      3
932       71291    1835      6
935       71299    1835      6
2946      72131    1835      6
2947      72139    1835      6
4576      72049    1835      6
4577      72041    1835      6
30        64141    1837      2
1079      64139    1837      2
300       67521    1839      8
1578      67511    1839      8
1675      67509    1839      8
2215      67131    1839      8
2415      67529    1839      8
3318      67531    1839      8
3319      67539    1839      8
4626      67519    1839      8
414       65161    1840     10
1629      65151    1840     10
1653      65169    1840     10
1803      65079    1840     10
2115      65159    1840     10
2959      65191    1840     10
3619      65199    1840     10
4309      65241    1840     10
4313      65249    1840     10
4697      65071    1840     10
2687      65481    1841      4
2688      65489    1841      4
3323      65109    1841      4
3336      65101    1841      4
1240      65639    1842      5
3602      65681    1842      5
4339      65139    1842      5
4964      65689    1842      5
4966      65661    1842      5
855       92131    1853     13
859       92139    1853     13
1952      92061    1853     13
2326      92069    1853     13
3097      92201    1853     13
3508      92301    1853     13
3583      92279    1853     13
3777      83301    1853     13
3996      83309    1853     13
4146      92309    1853     13
4350      92271    1853     13
4443      92209    1853     13
4471      92141    1853     13
487       83321    1854      8
1147      83049    1854      8
1712      83059    1854      8
2651      83011    1854      8
3243      83062    1854      8
3249      83031    1854      8
4099      83141    1854      8
4447      83329    1854      8
1906      84511    1855      9
2608      72081    1855      9
2609      72089    1855      9
3557      72071    1855      9
3600      72079    1855      9
4578      72039    1855      9
4579      72031    1855      9
4580      72061    1855      9
4582      72069    1855      9
4027      64151    1858      3
4178      64159    1858      3
5065      64149    1858      3
89        67661    1860      1
83        65271    1861     10
407       65319    1861     10
485       65311    1861     10
698       65309    1861     10
2391      65289    1861     10
2632      65281    1861     10
2744      65381    1861     10
2745      65389    1861     10
3358      65301    1861     10
3521      65279    1861     10
1070      65129    1862      3
1366      65119    1862      3
2462      65111    1862      3
1579      92191    1874      7
2977      92229    1874      7
3021      92221    1874      7
3023      92231    1874      7
3025      92239    1874      7
4445      92289    1874      7
4681      92199    1874      7
2479      83129    1875      2
4748      83121    1875      2
1656      83341    1876      6
1716      83331    1876      6
2367      83361    1876      6
3149      83351    1876      6
4335      83381    1876      6
4901      83371    1876      6
349       84701    1877     10
2008      84491    1877     10
2557      84499    1877     10
2944      72149    1877     10
2945      72141    1877     10
3039      72151    1877     10
3041      72159    1877     10
4575      84709    1877     10
4884      84489    1877     10
4885      84481    1877     10
1299      64189    1880      6
1477      64181    1880      6
2418      64161    1880      6
3609      64179    1880      6
4747      64171    1880      6
4941      64169    1880      6
1385      65239    1882      9
1628      65269    1882      9
1904      65261    1882      9
2280      65231    1882      9
2607      65171    1882      9
2935      65429    1882      9
2936      65419    1882      9
3442      65411    1882      9
3693      65179    1882      9
3248      65399    1883      2
3257      65391    1883      2
34        92089    1895     11
299       93059    1895     11
428       92081    1895     11
442       93051    1895     11
884       92151    1895     11
2071      92149    1895     11
2384      92159    1895     11
2976      92219    1895     11
3020      92071    1895     11
3022      92211    1895     11
3024      92079    1895     11
376       83099    1896     10
441       83191    1896     10
988       83201    1896     10
1080      83199    1896     10
1932      83079    1896     10
2370      83189    1896     10
2508      83081    1896     10
2527      83209    1896     10
3238      83063    1896     10
4289      83181    1896     10
1371      84501    1897      2
4511      84539    1897      2
3040      72161    1898      2
3042      72169    1898      2
3076      73029    1901      4
3081      73021    1901      4
3084      64199    1901      4
3085      64191    1901      4
549       65321    1903      4
873       65329    1903      4
3237      65371    1903      4
3246      65379    1903      4
1040      93189    1916      3
3296      93179    1916      3
4682      93181    1916      3
510       83239    1917     12
1088      83231    1917     12
1228      93101    1917     12
1559      83171    1917     12
1799      93109    1917     12
2009      93111    1917     12
2230      93119    1917     12
2596      83229    1917     12
3611      93069    1917     12
4790      93061    1917     12
4804      83219    1917     12
4853      83179    1917     12
833       84561    1918     10
834       84551    1918     10
1793      84559    1918     10
2097      84579    1918     10
2127      84641    1918     10
2327      84649    1918     10
2930      84589    1918     10
2931      84581    1918     10
3106      84571    1918     10
4891      84569    1918     10
290       84479    1919      6
674       84471    1919      6
1265      84469    1919      6
1507      84459    1919      6
1819      84461    1919      6
5131      84451    1919      6
3077      74019    1922      5
3079      74011    1922      5
3082      73031    1922      5
3083      73039    1922      5
3869      75391    1922      5
647       65189    1924      4
2997      65561    1924      4
2998      65569    1924      4
3241      65181    1924      4
819       93129    1937      8
3228      93121    1937      8
3295      93171    1937      8
3593      93021    1937      8
4122      93011    1937      8
4785      93199    1937      8
4855      93019    1937      8
5037      93029    1937      8
22        84029    1938     11
108       84011    1938     11
259       84021    1938     11
569       83251    1938     11
607       83269    1938     11
908       83261    1938     11
1434      83271    1938     11
1980      84019    1938     11
2045      83281    1938     11
2793      83279    1938     11
5007      83249    1938     11
21        84409    1939      8
193       84369    1939      8
573       84371    1939      8
880       84361    1939      8
1947      84381    1939      8
2157      84391    1939      8
2192      84379    1939      8
4244      84401    1939      8
3078      74021    1942      4
3080      74029    1942      4
3310      74039    1942      4
3311      74031    1942      4
2614      93169    1958      1
63        93089    1959      4
465       93071    1959      4
854       93079    1959      4
5004      93081    1959      4
823       84031    1960     11
984       84311    1960     11
1680      84541    1960     11
1869      84549    1960     11
3671      84319    1960     11
3754      84008    1960     11
3755      84009    1960     11
3844      84091    1960     11
4728      84309    1960     11
4732      84301    1960     11
4877      84039    1960     11
382       84619    1961      6
589       84621    1961      6
2264      84639    1961      6
2539      84629    1961      6
3922      84611    1961      6
4533      84631    1961      6
983       75031    1962      9
985       75021    1962      9
1152      75039    1962      9
1332      75241    1962      9
2870      75259    1962      9
2990      75401    1962      9
2991      75409    1962      9
4304      75251    1962      9
4914      75249    1962      9
1491      75381    1964      1
694       93039    1979      8
906       93031    1979      8
919       93159    1979      8
1913      93151    1979      8
2275      93201    1979      8
2295      93161    1979      8
2709      93149    1979      8
3931      93049    1979      8
927       84139    1980      6
1492      84161    1980      6
1916      84131    1980      6
2037      84129    1980      6
2194      84121    1980      6
2942      84169    1980      6
336       84321    1981     12
480       84411    1981     12
496       84329    1981     12
1323      84339    1981     12
1478      84429    1981     12
1505      84449    1981     12
2474      84349    1981     12
2547      84421    1981     12
4423      84341    1981     12
4651      84331    1981     12
4851      84419    1981     12
4972      84521    1981     12
1832      75239    1982      1
994       75151    1983     11
1055      75379    1983     11
1522      75159    1983     11
2105      75141    1983     11
2515      75371    1983     11
2567      75111    1983     11
2988      75411    1983     11
2989      75419    1983     11
3762      75179    1983     11
3763      75171    1983     11
4605      75149    1983     11
553       75319    1984     10
1928      75361    1984     10
2992      75469    1984     10
2993      75461    1984     10
3018      75369    1984     10
3058      74041    1984     10
3059      74049    1984     10
3308      74051    1984     10
3309      74059    1984     10
4633      75311    1984     10
2007      77331    1985      2
3279      77339    1985      2
215       94029    2001     10
479       84159    2001     10
670       93091    2001     10
737       93139    2001     10
789       94011    2001     10
1484      93041    2001     10
1485      94019    2001     10
1545      93131    2001     10
2369      84151    2001     10
4904      93099    2001     10
1309      84191    2002      7
2300      84219    2002      7
2383      84049    2002      7
3026      84351    2002      7
3027      84359    2002      7
3575      84199    2002      7
4098      84041    2002      7
888       75349    2003      6
1084      75341    2003      6
2379      84609    2003      6
2873      84201    2003      6
3066      84209    2003      6
4324      84601    2003      6
46        75201    2004     15
209       75169    2004     15
651       75101    2004     15
1031      75209    2004     15
1413      75109    2004     15
1414      75081    2004     15
1573      75231    2004     15
1577      75089    2004     15
2032      75161    2004     15
2047      75219    2004     15
2447      75071    2004     15
3045      76049    2004     15
3262      75079    2004     15
3306      76041    2004     15
4845      75099    2004     15
245       75291    2005     11
276       75501    2005     11
286       75509    2005     11
1043      75339    2005     11
1474      75299    2005     11
2725      75279    2005     11
2761      75289    2005     11
3089      75511    2005     11
3090      75519    2005     11
3589      75281    2005     11
4417      75271    2005     11
2146      75351    2006      2
2154      75359    2006      2
869       77261    2007      2
2096      77269    2007      2
825       84111    2022      6
1273      84119    2022      6
1883      84089    2022      6
2358      84149    2022      6
3578      84141    2022      6
4185      84081    2022      6
654       84211    2023      9
1264      84239    2023      9
1399      84259    2023      9
1494      84251    2023      9
1739      84529    2023      9
2093      84231    2023      9
4623      84249    2023      9
4890      84229    2023      9
4973      84221    2023      9
390       75061    2024      7
490       75229    2024      7
645       75069    2024      7
1261      75221    2024      7
5097      76289    2024      7
5125      75059    2024      7
5128      75051    2024      7
1376      75131    2025      9
1726      75139    2025      9
1777      75329    2025      9
2006      75261    2025      9
3047      76529    2025      9
3223      76521    2025      9
3312      75129    2025      9
3532      75121    2025      9
4041      75269    2025      9
3088      75481    2026      4
3714      75499    2026      4
3730      75491    2026      4
3732      75488    2026      4
195       77251    2027     14
249       77221    2027     14
678       77281    2027     14
1095      77219    2027     14
1713      77319    2027     14
1879      77161    2027     14
1888      77279    2027     14
2270      77311    2027     14
2680      77169    2027     14
2681      77231    2027     14
2975      77291    2027     14
4022      77239    2027     14
4606      77289    2027     14
4907      77271    2027     14
959       94089    2043      4
4128      94021    2043      4
4667      94039    2043      4
4668      94031    2043      4
1243      84241    2044      6
1548      84069    2044      6
1983      84281    2044      6
2228      84051    2044      6
3625      84061    2044      6
4704      84289    2044      6
604       84271    2045      1
1938      76131    2046     11
2416      76139    2046     11
3313      76119    2046     11
3314      76059    2046     11
3315      76051    2046     11
3316      76111    2046     11
3648      76069    2046     11
4981      76061    2046     11
5096      76281    2046     11
5126      76129    2046     11
5127      76121    2046     11
2721      76519    2047      7
2759      76541    2047      7
3046      76511    2047      7
3576      75571    2047      7
3577      75579    2047      7
4050      75479    2047      7
4055      75471    2047      7
314       77249    2048     11
1814      77181    2048     11
2057      77301    2048     11
2218      77309    2048     11
3068      77241    2048     11
3171      78049    2048     11
3708      77019    2048     11
4147      77061    2048     11
4395      77189    2048     11
4398      77069    2048     11
4567      77011    2048     11
127       77259    2049      2
2981      77129    2049      2
431       84661    2064     10
874       84679    2064     10
1365      84071    2064     10
1418      84079    2064     10
1468      84681    2064     10
1892      84691    2064     10
2616      84671    2064     10
4425      84669    2064     10
4559      84101    2064     10
4560      84109    2064     10
712       85061    2065      5
746       85081    2065      5
2046      85069    2065      5
2190      84269    2065      5
3820      84261    2065      5
3341      76339    2066      1
373       76191    2067     12
417       76151    2067     12
1198      75019    2067     12
1320      75009    2067     12
1728      75008    2067     12
1965      76149    2067     12
2553      76159    2067     12
3415      76141    2067     12
3416      76199    2067     12
4046      76209    2067     12
4497      76559    2067     12
4791      76551    2067     12
2540      77389    2068      7
3560      75541    2068      7
3571      75569    2068      7
3579      75559    2068      7
3664      75551    2068      7
4620      75549    2068      7
4631      75561    2068      7
38        77099    2069     11
377       77199    2069     11
754       77079    2069     11
946       77089    2069     11
961       77209    2069     11
1345      77201    2069     11
1963      77211    2069     11
3928      77081    2069     11
4052      77071    2069     11
4269      77191    2069     11
4409      77091    2069     11
67        94049    2085      4
2064      94059    2085      4
3703      94051    2085      4
4908      94041    2085      4
3650      85099    2086      2
3651      85091    2086      2
1105      84591    2087      7
1501      96109    2087      7
2106      84599    2087      7
2195      84299    2087      7
2355      84279    2087      7
5110      96289    2087      7
5122      96281    2087      7
265       76179    2088      8
772       76081    2088      8
1636      76071    2088      8
1826      76089    2088      8
1851      76079    2088      8
2108      76161    2088      8
4431      76169    2088      8
5023      76171    2088      8
591       76361    2089      4
867       76399    2089      4
4555      76369    2089      4
4621      76391    2089      4
154       77131    2090     17
494       77179    2090     17
1257      77008    2090     17
1387      77009    2090     17
1694      77321    2090     17
2346      77139    2090     17
2381      77021    2090     17
2537      77381    2090     17
3100      77371    2090     17
3234      77379    2090     17
3250      77141    2090     17
3255      77329    2090     17
3261      77329    2090     17
3263      77029    2090     17
4773      77171    2090     17
4870      77039    2090     17
5080      77031    2090     17
1245      77111    2091      2
2182      77119    2091      2
1765      94099    2105      1
260       94009    2106      3
1210      94061    2106      3
1923      94069    2106      3
130       85101    2107     13
359       84431    2107     13
930       85059    2107     13
957       85109    2107     13
1821      96011    2107     13
1970      85079    2107     13
2171      96111    2107     13
3251      96119    2107     13
3771      85051    2107     13
4489      84439    2107     13
4637      85071    2107     13
4646      96019    2107     13
5089      85089    2107     13
643       96159    2108      9
680       96169    2108      9
1953      96141    2108      9
2427      96151    2108      9
2667      96161    2108      9
3282      96149    2108      9
4830      76329    2108      9
5120      96251    2108      9
5121      96259    2108      9
745       76201    2109     10
1283      76471    2109     10
1574      76401    2109     10
3111      76181    2109     10
3112      76189    2109     10
3700      76409    2109     10
4585      76219    2109     10
4660      76221    2109     10
4661      76229    2109     10
4662      76211    2109     10
315       77369    2110      8
1483      77341    2110      8
1594      77361    2110      8
1806      77041    2110      8
3892      77359    2110      8
4123      77351    2110      8
4868      77349    2110      8
4869      77049    2110      8
1915      77101    2111      2
4742      77109    2111      2
565       85031    2128      5
1719      85049    2128      5
2141      85039    2128      5
3930      85029    2128      5
4127      85041    2128      5
4         96081    2129      5
1556      96071    2129      5
2343      96089    2129      5
2641      96101    2129      5
3244      96079    2129      5
615       96131    2130      7
1440      76291    2130      7
1708      76099    2130      7
2332      76091    2130      7
2662      76101    2130      7
4411      76301    2130      7
4898      76109    2130      7
1248      76389    2131     10
1848      76351    2131     10
2016      76349    2131     10
2056      76359    2131     10
2087      76261    2131     10
2543      76271    2131     10
2581      76371    2131     10
2908      76279    2131     10
3113      76341    2131     10
4182      76269    2131     10
448       78109    2132      5
1623      78089    2132      5
2481      78101    2132      5
2486      78241    2132      5
5025      78081    2132      5
778       85021    2148      4
2167      85019    2148      4
4383      94079    2148      4
4843      94071    2148      4
1383      96029    2149      8
2291      96231    2149      8
2600      96221    2149      8
3264      96319    2149      8
3265      96319    2149      8
3990      96021    2149      8
4217      96311    2149      8
4493      96229    2149      8
10        96139    2150     13
1085      96171    2150     13
1164      96121    2150     13
2052      96129    2150     13
2181      96191    2150     13
2382      96189    2150     13
2555      96181    2150     13
2569      96199    2150     13
3267      96269    2150     13
3381      96299    2150     13
3838      96261    2150     13
4375      96291    2150     13
4803      96179    2150     13
53        76319    2151     14
695       76461    2151     14
1811      76419    2151     14
2301      76429    2151     14
3043      76031    2151     14
3044      76039    2151     14
3102      76311    2151     14
3110      76411    2151     14
3392      76241    2151     14
3398      76249    2151     14
3769      76421    2151     14
3845      76469    2151     14
4880      76231    2151     14
4881      76239    2151     14
206       78071    2152     12
324       78069    2152     12
783       78161    2152     12
1285      78179    2152     12
1354      78079    2152     12
1472      78189    2152     12
2531      78181    2152     12
2568      77059    2152     12
3287      78061    2152     12
4138      78171    2152     12
4191      78169    2152     12
4618      77051    2152     12
827       78119    2153      8
1517      78091    2153      8
1977      78269    2153      8
3178      78261    2153      8
3240      78099    2153      8
3512      78251    2153      8
3513      78259    2153      8
4802      78111    2153      8
2932      96411    2171     15
2951      95909    2171     15
2952      95901    2171     15
2953      96449    2171     15
2954      96441    2171     15
2955      96041    2171     15
2956      96049    2171     15
2994      96419    2171     15
3035      96201    2171     15
3036      96209    2171     15
3757      96301    2171     15
4863      96039    2171     15
4865      96091    2171     15
4947      96031    2171     15
4953      96099    2171     15
125       96061    2172      5
229       76449    2172      5
929       76451    2172      5
2165      76459    2172      5
2698      76441    2172      5
617       98081    2173      8
1475      78199    2173      8
1604      78191    2173      8
1971      76251    2173      8
3114      76259    2173      8
3673      98011    2173      8
4334      98089    2173      8
4977      98019    2173      8
28        78221    2174     11
133       78231    2174     11
155       78121    2174     11
1101      78131    2174     11
1350      78229    2174     11
1405      78129    2174     11
1442      78209    2174     11
2412      78139    2174     11
4273      78159    2174     11
4619      78201    2174     11
4622      78151    2174     11
375       96271    2191      9
775       96321    2191      9
1807      96239    2191      9
2987      96389    2191      9
3756      96381    2191      9
3758      96309    2191      9
4214      96331    2191      9
4299      96371    2191      9
4591      96329    2191      9
2982      96051    2192      4
2983      96059    2192      4
3038      97009    2192      4
3590      96069    2192      4
926       76431    2193      6
1564      98291    2193      6
1647      98299    2193      6
2404      76439    2193      6
2635      97011    2193      6
4102      97019    2193      6
43        98099    2194     14
970       78219    2194     14
997       98029    2194     14
1051      78059    2194     14
2289      98091    2194     14
2852      98109    2194     14
2857      98111    2194     14
2860      98101    2194     14
3212      78149    2194     14
3218      98119    2194     14
3219      78141    2194     14
3586      78051    2194     14
3617      78211    2194     14
4976      98021    2194     14
216       78279    2195      2
4372      78271    2195      2
2626      96241    2212      2
4475      96249    2212      2
75        96391    2213      3
3037      96401    2213      3
4218      96361    2213      3
516       97169    2214      7
1123      97159    2214      7
1745      97149    2214      7
1748      97141    2214      7
1898      97151    2214      7
2468      97161    2214      7
3220      97301    2214      7
271       97051    2215     12
316       97119    2215     12
383       97101    2215     12
488       98311    2215     12
784       97111    2215     12
875       97121    2215     12
1103      97129    2215     12
1886      97059    2215     12
2390      98319    2215     12
4503      98301    2215     12
4588      98309    2215     12
4723      97109    2215     12
1077      98121    2216      2
4629      98129    2216      2
2536      96351    2233      2
4592      96341    2233      2
954       97189    2234      3
1460      97179    2234      3
1874      97171    2234      3
2110      97049    2235      4
3770      97041    2235      4
4500      97031    2235      4
5148      97039    2235      4
232       98039    2236      4
1336      98049    2236      4
1809      98041    2236      4
2328      98031    2236      4
896       98219    2237      2
3937      98209    2237      2
1359      97181    2256      2
3580      97311    2256      2
721       97201    2257      3
2180      97209    2257      3
3342      97321    2257      3
226       98149    2258     11
891       98059    2258     11
1297      98139    2258     11
1759      98069    2258     11
1847      98131    2258     11
1934      98141    2258     11
2030      98051    2258     11
2392      97099    2258     11
2593      98231    2258     11
4942      98239    2258     11
4980      97091    2258     11
1211      98181    2259      3
1417      98199    2259      3
2265      98171    2259      3
3403      97331    2277      1
153       97069    2278      5
1735      97061    2278      5
1937      97079    2278      5
2038      97079    2278      5
2039      97071    2278      5
231       98079    2279      6
1116      98161    2279      6
1190      98151    2279      6
2538      98061    2279      6
4432      98229    2279      6
5038      98071    2279      6
842       99089    2280      5
980       99081    2280      5
1094      99091    2280      5
1488      99071    2280      5
2475      99099    2280      5
843       95209    2297      2
5119      95159    2297      2
37        97089    2300      2
2371      97081    2300      2
1295      99031    2301      7
1487      99079    2301      7
1663      99011    2301      7
1941      99029    2301      7
1985      99019    2301      7
2323      99039    2301      7
4892      99021    2301      7
121       95151    2318      3
835       95019    2318      3
2450      95011    2318      3
1454      95109    2319      1
443       99101    2322      8
614       99119    2322      8
716       99041    2322      8
1722      99131    2322      8
3622      99111    2322      8
3667      99109    2322      8
4427      99129    2322      8
5028      99009    2322      8
571       96219    2337      1
709       95029    2341      1
803       99049    2343      3
1423      99139    2343      3
4355      99181    2343      3
1662      95129    2361      1
626       99171    2364      4
1676      99161    2364      4
3677      99189    2364      4
4905      95079    2364      4
3071      96429    2379      2
3072      96421    2379      2
562       95049    2384      4
2067      95051    2384      4
3544      95041    2384      4
3637      95039    2384      4
402       95141    2405      6
560       95149    2405      6
3853      95061    2405      6
3854      95069    2405      6
4315      95191    2405      6
4594      95189    2405      6
483       95089    2406      4
595       95071    2406      4
3968      95099    2406      4
4113      95081    2406      4
2207      95171    2426      5
2248      95179    2426      5
3494      95169    2426      5
4225      95161    2426      5
4504      95181    2426      5
1524      95131    2427      3
3906      95091    2427      3
5061      95139    2427      3
3063      96439    2505      2
3073      96431    2505      2

5.2 Combine odbus6_9 with od_data

For further visual operation, we need to combine a table contains the number of trips between pairs of origin and destination hexagons.

Code 
od_data <- left_join(odbus6_9, honeycomb_grid,
                      by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  rename(ORIGIN_BS = ORIGIN_PT_CODE,
         ORIGIN_SZ = grid_id,
         DESTIN_BS = DESTINATION_PT_CODE)

Before continue, check for duplicating records.

Code 
duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

Another left join between odbus6_9 and honeycomb_grid to get the DESTIN_BS.

Code 
od_data <- left_join(od_data, honeycomb_grid, 
                           by = c("DESTIN_BS" = "BUS_STOP_N")) %>%
  rename(DESTIN_SZ = grid_id)

Before continue, check for duplicating records.

Code 
duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

Group by ‘ORIGIN_GRID_ID’ and ‘DESTIN_GRID_ID’ to create a new column ‘MORNING_PEAK’ representing the total number of trips between each pair of hexagons.

Code 
od_data <- od_data %>%
  drop_na() %>%
  group_by(ORIGIN_SZ, DESTIN_SZ) %>%
  summarise(MORNING_PEAK = sum(TRIPS))

6 Visualising Spatial Interaction

6.1 Removing intra-zonal flows

We will not plot the intra-zonal flows. The code chunk below will be used to remove intra-zonal flows.

Code 
od_data1 <- od_data[od_data$ORIGIN_SZ!=od_data$DESTIN_SZ,]

6.2 Create flowline

Code 
flowLine <- od2line(flow = od_data1, 
                    zones = bs_num,
                    zone_code = "grid_id")

6.3 Visualisation and Analysis

Code 
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
  tm_borders(alpha=0.7,col = "white")+
  tm_polygons("darkgrey") +
tm_shape(bs_num) +
  tm_fill("num_bs",alpha=0.8,palette = "Greens")+
  tm_polygons() +
flowLine %>%  
  filter(MORNING_PEAK >= 5000) %>%
tm_shape() +
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.3,3, 6, 9, 12, 18,21, 27),
           n = 6,
           alpha = 0.5,
           col="yellow") +
  tm_layout(main.title = 'OD Flow On Weekday Morning Peak hour' ,
            main.title.position = "center",
            main.title.size = 1,
            main.title.fontface = 'bold') +
  tm_compass(type="8star", size = 1) +
  tm_scale_bar()

In this map, we filtered out trips with a count less than 5000 for enhanced analysis. Thicker flowlines indicate a higher volume of trips, while the length of the flowlines represents the distance between each hexagon. Notably, we observe long lines from the northern to the eastern regions, which, upon referencing the Singapore subway map, suggests a lack of subway connections along that route. Additionally, thicker lines predominantly appear in darker-colored hexagons, indicating a positive correlation between the number of bus stations and trip volume.

Code 
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
  tm_borders(alpha=0.7,col = "white")+
  tm_polygons("darkgrey") +

tm_shape(bs_num %>%
  filter(num_bs <= 3)) +
  tm_fill("num_bs",alpha=0.8,palette = "Greens")+
  tm_polygons() +

tm_shape(flowLine %>%  
  filter(MORNING_PEAK >= 20000)) +
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.3,3, 6, 9, 12, 18,21, 27),
           n = 6,
           alpha = 0.5,
           col="yellow") +
  tm_layout(main.title = 'OD Flow On Weekday Morning Peak hour' ,
            main.title.position = "center",
            main.title.size = 1,
            main.title.fontface = 'bold') +
  tm_compass(type="8star", size = 1) +
  tm_scale_bar()

After filtering for bus stops with a count of 3 or fewer and trips exceeding 20000, we observe a significant reduction in the overlap between flow lines and hexagons. This confirms the earlier understanding of the relationship between bus stations and trip volume. However, notable overlaps persist in the northern part of Singapore. Given the geographical context, this is likely attributed to buses traveling between Malaysia and Singapore—routes with fewer stations but higher trip volumes.

7 Assemble propulsive and attractiveness variables

Business

Code 
business <- st_read(dsn = "data/geospatial",
                   layer = "Business") %>%
  st_transform(crs = 3414)
Reading layer `Business' from data source 
  `C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 6550 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3669.148 ymin: 25408.41 xmax: 47034.83 ymax: 50148.54
Projected CRS: SVY21 / Singapore TM
Code 
bs_num$`BUSINESS_num`<- lengths(
  st_intersects(
    bs_num, business))
Code 
summary(bs_num$BUSINESS_num)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   1.000   7.273   7.000  97.000
Code 
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
  tm_borders(alpha=0.7,col = "white")+
  tm_polygons("darkgrey") +

tm_shape(bs_num) +
  tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(business) +
  tm_dots(size = 0.05, col = "yellow")

F&B

Code 
fb <- st_read(dsn = "data/geospatial",                    layer = "F&B") %>%   st_transform(crs = 3414)
Reading layer `F&B' from data source 
  `C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 1919 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6010.495 ymin: 25343.27 xmax: 45462.43 ymax: 48796.21
Projected CRS: SVY21 / Singapore TM
Code 
bs_num$`FB_num`<- lengths(   
  st_intersects(     
    bs_num, fb))
Code 
summary(bs_num$FB_num)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   2.204   1.000 133.000
Code 
tmap_mode("plot") 
tmap_options(check.and.fix = TRUE) 
tm_shape(mpsz) +   
  tm_borders(alpha=0.7,col = "white")+   
  tm_polygons("darkgrey") +  tm_shape(bs_num) +   
  tm_polygons(alpha=0.5, col = "darkgreen")+ 
  tm_shape(fb) +   
  tm_dots(size = 0.05, col = "yellow")

Leisure&Recreation

Code 
lr <- st_read(dsn = "data/geospatial",                    
              layer = "Liesure&Recreation") %>%   
  st_transform(crs = 3414)
Reading layer `Liesure&Recreation' from data source 
  `C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 1217 features and 30 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6010.495 ymin: 25134.28 xmax: 48439.77 ymax: 50078.88
Projected CRS: SVY21 / Singapore TM
Code 
bs_num$`lr_num`<- lengths(   
  st_intersects(     
    bs_num, lr))
Code 
summary(bs_num$lr_num)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   1.307   1.000  41.000
Code 
tmap_mode("plot") 
tmap_options(check.and.fix = TRUE) 
tm_shape(mpsz) +   
  tm_borders(alpha=0.7,col = "white")+   
  tm_polygons("darkgrey") +  tm_shape(bs_num) +   
  tm_polygons(alpha=0.5, col = "darkgreen")+ 
  tm_shape(lr) +   
  tm_dots(size = 0.05, col = "yellow")

schools

Code 
schools <- read_csv("data/aspatial/schools.csv") %>%
  rename(latitude = "results.LATITUDE",
         longitude = "results.LONGITUDE")%>%
  select(postal_code, school_name, latitude, longitude)
Code 
schools_sf <- st_as_sf(schools, 
                       coords = c("longitude", "latitude"),
                       crs=4326) %>%
  st_transform(crs = 3414)
Code 
bs_num$`schools_num`<- lengths(   
  st_intersects(     
    bs_num, schools_sf))
Code 
summary(bs_num$schools_num)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.4125  1.0000  4.0000
Code 
tmap_mode("plot") 
tmap_options(check.and.fix = TRUE) 
tm_shape(mpsz) +   
  tm_borders(alpha=0.7,col = "white")+   
  tm_polygons("darkgrey") +  tm_shape(bs_num) +   
  tm_polygons(alpha=0.5, col = "darkgreen")+ 
  tm_shape(schools_sf) +   
  tm_dots(size = 0.05, col = "yellow")

HDB

Code 
hdb <- read_csv("data/aspatial/hdb.csv") %>%
  rename(latitude = "lat",
         longitude = "lng")
Code 
hdb_sf <- st_as_sf(hdb, 
                       coords = c("longitude", "latitude"),
                       crs=4326) %>%
  st_transform(crs = 3414)
Code 
bs_num$`hdb_num`<- lengths(   
  st_intersects(     
    bs_num, hdb_sf))
Code 
summary(bs_num$hdb_num)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   0.00    0.00    0.00   14.85   27.00  103.00
Code 
tmap_mode("plot") 
tmap_options(check.and.fix = TRUE) 
tm_shape(mpsz) +   
  tm_borders(alpha=0.7,col = "white")+   
  tm_polygons("darkgrey") +  tm_shape(bs_num) +   
  tm_polygons(alpha=0.5, col = "darkgreen")+ 
  tm_shape(hdb_sf) +   
  tm_dots(size = 0.05, col = "yellow")

Entertainment

Code 
entertn <- st_read(dsn = "data/geospatial",
                   layer = "entertn") %>%
  st_transform(crs = 3414)
Reading layer `entertn' from data source 
  `C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 114 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 10809.34 ymin: 26528.63 xmax: 41600.62 ymax: 46375.77
Projected CRS: SVY21 / Singapore TM
Code 
bs_num$`entertn_num`<- lengths(
  st_intersects(
    bs_num, entertn))
Code 
summary(bs_num$entertn_num)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.1331  0.0000  9.0000
Code 
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
  tm_borders(alpha=0.7,col = "white")+
  tm_polygons("darkgrey") +

tm_shape(bs_num) +
  tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(entertn) +
  tm_dots(size = 0.05, col = "yellow")

The data will be joined with :

Code 
bs_num_tidy <- bs_num %>%
  st_drop_geometry() %>%
  select(grid_id, BUSINESS_num, FB_num, lr_num, schools_num,  hdb_num, entertn_num )
Code 
flow_data <- od_data1 %>%
  left_join(bs_num_tidy,
            by = c("DESTIN_SZ" = "grid_id"))
Code 
summary(flow_data)
   ORIGIN_SZ      DESTIN_SZ     MORNING_PEAK      BUSINESS_num   
 Min.   :  23   Min.   :  23   Min.   :    1.0   Min.   : 0.000  
 1st Qu.:1099   1st Qu.:1116   1st Qu.:    7.0   1st Qu.: 0.000  
 Median :1433   Median :1432   Median :   38.0   Median : 1.000  
 Mean   :1416   Mean   :1414   Mean   :  385.1   Mean   : 7.302  
 3rd Qu.:1728   3rd Qu.:1711   3rd Qu.:  180.0   3rd Qu.: 6.000  
 Max.   :2505   Max.   :2505   Max.   :96644.0   Max.   :97.000  
     FB_num            lr_num        schools_num        hdb_num      
 Min.   :  0.000   Min.   : 0.000   Min.   :0.0000   Min.   :  0.00  
 1st Qu.:  0.000   1st Qu.: 0.000   1st Qu.:0.0000   1st Qu.:  0.00  
 Median :  0.000   Median : 1.000   Median :0.0000   Median : 10.00  
 Mean   :  5.776   Mean   : 2.368   Mean   :0.5291   Mean   : 19.39  
 3rd Qu.:  2.000   3rd Qu.: 3.000   3rd Qu.:1.0000   3rd Qu.: 34.00  
 Max.   :133.000   Max.   :41.000   Max.   :4.0000   Max.   :103.00  
  entertn_num   
 Min.   :0.000  
 1st Qu.:0.000  
 Median :0.000  
 Mean   :0.336  
 3rd Qu.:0.000  
 Max.   :9.000

We can see there are 0 values in BUSINESS_num, FB_num, lr_num, schools_num, hdb_num, entertn_num.

The code chunk below will be used to replace zero values to 0.99 for the propulsive and attractiveness variables.

Code 
flow_data$BUSINESS_num <- ifelse(
  flow_data$BUSINESS_num == 0,
  0.99, flow_data$BUSINESS_num)
flow_data$FB_num <- ifelse(
  flow_data$FB_num == 0,
  0.99, flow_data$FB_num)
flow_data$lr_num <- ifelse(
  flow_data$lr_num == 0,
  0.99, flow_data$lr_num)
flow_data$schools_num <- ifelse(
  flow_data$schools_num == 0,
  0.99, flow_data$schools_num)
flow_data$hdb_num <- ifelse(
  flow_data$hdb_num == 0,
  0.99, flow_data$hdb_num)
flow_data$entertn_num<- ifelse(
  flow_data$entertn_num == 0,
  0.99, flow_data$entertn_num)
Code 
summary(flow_data)
   ORIGIN_SZ      DESTIN_SZ     MORNING_PEAK      BUSINESS_num   
 Min.   :  23   Min.   :  23   Min.   :    1.0   Min.   : 0.990  
 1st Qu.:1099   1st Qu.:1116   1st Qu.:    7.0   1st Qu.: 0.990  
 Median :1433   Median :1432   Median :   38.0   Median : 1.000  
 Mean   :1416   Mean   :1414   Mean   :  385.1   Mean   : 7.729  
 3rd Qu.:1728   3rd Qu.:1711   3rd Qu.:  180.0   3rd Qu.: 6.000  
 Max.   :2505   Max.   :2505   Max.   :96644.0   Max.   :97.000  
     FB_num            lr_num        schools_num       hdb_num      
 Min.   :  0.990   Min.   : 0.990   Min.   :0.990   Min.   :  0.99  
 1st Qu.:  0.990   1st Qu.: 0.990   1st Qu.:0.990   1st Qu.:  0.99  
 Median :  0.990   Median : 1.000   Median :0.990   Median : 10.00  
 Mean   :  6.306   Mean   : 2.769   Mean   :1.171   Mean   : 19.76  
 3rd Qu.:  2.000   3rd Qu.: 3.000   3rd Qu.:1.000   3rd Qu.: 34.00  
 Max.   :133.000   Max.   :41.000   Max.   :4.000   Max.   :103.00  
  entertn_num   
 Min.   :0.990  
 1st Qu.:0.990  
 Median :0.990  
 Mean   :1.183  
 3rd Qu.:0.990  
 Max.   :9.000

Now, there is no zero values in our data.

Next we will remove duplicate record:

Code 
duplicate <- flow_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
Code 
flow_data <- unique(flow_data)
Code 
summary(flow_data)
   ORIGIN_SZ      DESTIN_SZ     MORNING_PEAK      BUSINESS_num   
 Min.   :  23   Min.   :  23   Min.   :    1.0   Min.   : 0.990  
 1st Qu.:1099   1st Qu.:1116   1st Qu.:    7.0   1st Qu.: 0.990  
 Median :1433   Median :1432   Median :   38.0   Median : 1.000  
 Mean   :1416   Mean   :1414   Mean   :  385.1   Mean   : 7.729  
 3rd Qu.:1728   3rd Qu.:1711   3rd Qu.:  180.0   3rd Qu.: 6.000  
 Max.   :2505   Max.   :2505   Max.   :96644.0   Max.   :97.000  
     FB_num            lr_num        schools_num       hdb_num      
 Min.   :  0.990   Min.   : 0.990   Min.   :0.990   Min.   :  0.99  
 1st Qu.:  0.990   1st Qu.: 0.990   1st Qu.:0.990   1st Qu.:  0.99  
 Median :  0.990   Median : 1.000   Median :0.990   Median : 10.00  
 Mean   :  6.306   Mean   : 2.769   Mean   :1.171   Mean   : 19.76  
 3rd Qu.:  2.000   3rd Qu.: 3.000   3rd Qu.:1.000   3rd Qu.: 34.00  
 Max.   :133.000   Max.   :41.000   Max.   :4.000   Max.   :103.00  
  entertn_num   
 Min.   :0.990  
 1st Qu.:0.990  
 Median :0.990  
 Mean   :1.183  
 3rd Qu.:0.990  
 Max.   :9.000

The following table is explanatory variables to be used in the Spatial Interaction Modelling:

No Explanatory Variables
1 Business
2 F&B
3 Leisure&Rrecreation
4 schools
5 HDB
6 Entertainment

8 Compute Distance Matrix

8.1 Converting from sf data.table to SpatialPolygonsDataFrame

First as.Spatial() will be used to convert bs_num from sf tibble data frame to SpatialPolygonsDataFrame of sp object as shown in the code chunk below. Computing distance matrix using sp than sf package.

Code 
bs_num_sp <- as(bs_num, "Spatial")

8.2 Computing the distance matrix

Next, spDists() of sp package will be used to compute the Euclidean distance between the centroids of the hexagonsn.

The following code calculates the pairwise distances between the bus stations represented by bs_num_sp. The spDists function from the sp package is employed for this purpose. The distances are computed based on the spatial coordinates of the bus stations, and the result is stored in the variable dist. The parameter longlat = FALSE indicates that the distances should be computed in the native coordinate system (not considering latitude and longitude as spherical coordinates).

Code 
dist <- spDists(bs_num_sp, 
                longlat = FALSE)
Code 
head(dist, n=c(10, 10))
          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
 [1,]    0.000  750.000 3269.174 1500.000 2704.163 3968.627 1299.038 2250.000
 [2,]  750.000    0.000 2598.076  750.000 1984.313 3269.174  750.000 1500.000
 [3,] 3269.174 2598.076    0.000 1984.313  750.000  750.000 2704.163 1500.000
 [4,] 1500.000  750.000 1984.313    0.000 1299.038 2598.076  750.000  750.000
 [5,] 2704.163 1984.313  750.000 1299.038    0.000 1299.038 1984.313  750.000
 [6,] 3968.627 3269.174  750.000 2598.076 1299.038    0.000 3269.174 1984.313
 [7,] 1299.038  750.000 2704.163  750.000 1984.313 3269.174    0.000 1299.038
 [8,] 2250.000 1500.000 1500.000  750.000  750.000 1984.313 1299.038    0.000
 [9,] 3436.932 2704.163  750.000 1984.313  750.000  750.000 2598.076 1299.038
[10,] 4683.748 3968.627 1500.000 3269.174 1984.313  750.000 3897.114 2598.076
          [,9]    [,10]
 [1,] 3436.932 4683.748
 [2,] 2704.163 3968.627
 [3,]  750.000 1500.000
 [4,] 1984.313 3269.174
 [5,]  750.000 1984.313
 [6,]  750.000  750.000
 [7,] 2598.076 3897.114
 [8,] 1299.038 2598.076
 [9,]    0.000 1299.038
[10,] 1299.038    0.000

8.3 Labelling column and row heanders of a distance matrix

First, we will create a list sorted according to the the distance matrix by grid_id.

Code 
grid_id_names <- bs_num$grid_id

Next we will attach grid_id to row and column for distance matrix matching ahead.

Code 
colnames(dist) <- paste0(grid_id_names)
rownames(dist) <- paste0(grid_id_names)

8.3 Pivoting distance value by Hexagon grid

We will pivot the distance matrix into a long table by using the row and column grid_id as show in the code chunk below.

The melt operation reshapes the matrix into a long format.

Code 
distPair <-  reshape2::melt(dist) %>%
  rename(dist = value)
head(distPair, 10)
   Var1 Var2     dist
1    23   23    0.000
2    44   23  750.000
3    46   23 3269.174
4    66   23 1500.000
5    67   23 2704.163
6    68   23 3968.627
7    86   23 1299.038
8    87   23 2250.000
9    88   23 3436.932
10   89   23 4683.748

8.4 Updating intra-zonal distances

First, we will select and find out the minimum value of the distance by using summary().

Code 
distPair %>%
  filter(dist > 0) %>%
  summary()
      Var1           Var2           dist      
 Min.   :  23   Min.   :  23   Min.   :  750  
 1st Qu.: 871   1st Qu.: 871   1st Qu.: 8352  
 Median :1324   Median :1324   Median :13332  
 Mean   :1269   Mean   :1269   Mean   :14162  
 3rd Qu.:1688   3rd Qu.:1688   3rd Qu.:18929  
 Max.   :2505   Max.   :2505   Max.   :44680

The minimum distance is about 750, indicating travelling to adjacent hexagon.

Next, a constant distance value of 300 (middle to edge is 325) added into intra-zones distance.

Code 
distPair$dist <- ifelse(distPair$dist == 0,
                        300, distPair$dist)

The code chunk below will be used to check the result data.frame.

Code 
distPair %>%   
  summary()
      Var1           Var2           dist      
 Min.   :  23   Min.   :  23   Min.   :  300  
 1st Qu.: 871   1st Qu.: 871   1st Qu.: 8250  
 Median :1324   Median :1324   Median :13332  
 Mean   :1269   Mean   :1269   Mean   :14145  
 3rd Qu.:1688   3rd Qu.:1688   3rd Qu.:18929  
 Max.   :2505   Max.   :2505   Max.   :44680

The code chunk below is used to rename the origin and destination fields.

Code 
distPair <- distPair %>%
  rename(ORIGIN_GRID_ID = Var1,
         DESTIN_GRID_ID = Var2)

distPair %>% head()
  ORIGIN_GRID_ID DESTIN_GRID_ID     dist
1             23             23  300.000
2             44             23  750.000
3             46             23 3269.174
4             66             23 1500.000
5             67             23 2704.163
6             68             23 3968.627
Code 
glimpse(distPair)
Rows: 695,556
Columns: 3
$ ORIGIN_GRID_ID <int> 23, 44, 46, 66, 67, 68, 86, 87, 88, 89, 90, 109, 110, 1…
$ DESTIN_GRID_ID <int> 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23,…
$ dist           <dbl> 300.000, 750.000, 3269.174, 1500.000, 2704.163, 3968.62…

9 Spatial Interaction Modelling

9.1 Preparing Flow Data

In general, we will calibrate separate Spatial Interaction Models for inter- and intra-zonal flows. we will focus our attention on inter-zonal flow. Hence, we need to exclude the intra-zonal flow from flow_data.

First, two new columns called FlowNoIntra and offset will be created by using the code chunk below.

Code 
flow_data$FlowNoIntra <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0, flow_data$MORNING_PEAK)
flow_data$offset <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0.000001, 1)

Now, we need to combine flow data with distance value:

Code 
flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)
distPair$ORIGIN_GRID_ID <- as.factor(distPair$ORIGIN_GRID_ID)
distPair$DESTIN_GRID_ID <- as.factor(distPair$DESTIN_GRID_ID)
Code 
flow_data1 <- flow_data %>%
  left_join (distPair,
             by = c("ORIGIN_SZ" = "ORIGIN_GRID_ID",
                    "DESTIN_SZ" = "DESTIN_GRID_ID"))

we need to remove duplicate:

Code 
duplicate <- flow_data1 %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
Code 
SIM_data <- unique(flow_data1)

According to the syntax used to derive values in FlowNoIntra field, all intra-zonal flow will be given a value of 0 or else the original flow values will be inserted.

Next, inter-zonal flow will be selected from flow_data and save into a new output data.frame called inter_zonal_flow by using the code chunk below.

Code 
inter_zonal_flow <- SIM_data %>%
  filter(FlowNoIntra > 0)
Code 
summary(inter_zonal_flow)
   ORIGIN_SZ       DESTIN_SZ      MORNING_PEAK      BUSINESS_num   
 1960   :  298   1474   :  347   Min.   :    1.0   Min.   : 0.990  
 1474   :  292   1452   :  339   1st Qu.:    7.0   1st Qu.: 0.990  
 1477   :  292   1516   :  326   Median :   38.0   Median : 1.000  
 1496   :  278   1960   :  295   Mean   :  385.1   Mean   : 7.729  
 1623   :  277   1477   :  294   3rd Qu.:  180.0   3rd Qu.: 6.000  
 1749   :  273   1494   :  292   Max.   :96644.0   Max.   :97.000  
 (Other):63252   (Other):63069                                     
     FB_num            lr_num        schools_num       hdb_num      
 Min.   :  0.990   Min.   : 0.990   Min.   :0.990   Min.   :  0.99  
 1st Qu.:  0.990   1st Qu.: 0.990   1st Qu.:0.990   1st Qu.:  0.99  
 Median :  0.990   Median : 1.000   Median :0.990   Median : 10.00  
 Mean   :  6.306   Mean   : 2.769   Mean   :1.171   Mean   : 19.76  
 3rd Qu.:  2.000   3rd Qu.: 3.000   3rd Qu.:1.000   3rd Qu.: 34.00  
 Max.   :133.000   Max.   :41.000   Max.   :4.000   Max.   :103.00  
                                                                    
  entertn_num     FlowNoIntra          offset       dist      
 Min.   :0.990   Min.   :    1.0   Min.   :1   Min.   :  750  
 1st Qu.:0.990   1st Qu.:    7.0   1st Qu.:1   1st Qu.: 3000  
 Median :0.990   Median :   38.0   Median :1   Median : 5408  
 Mean   :1.183   Mean   :  385.1   Mean   :1   Mean   : 6334  
 3rd Qu.:0.990   3rd Qu.:  180.0   3rd Qu.:1   3rd Qu.: 8842  
 Max.   :9.000   Max.   :96644.0   Max.   :1   Max.   :24784

9.2 Visualising the dependent variable

Code 
ggplot(data = inter_zonal_flow,
       aes(x = MORNING_PEAK)) +
  geom_histogram()

We can see that all ‘MORNING_PEAK’ values are all positive values and its distribution is highly skewed to the right side.

Next, let us visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.

Code 
ggplot(data = inter_zonal_flow,
       aes(x = dist,
           y = MORNING_PEAK)) +
  geom_point() +
  geom_smooth(method = lm)

Their relationship hardly resemble linear relationship.

When we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.

Code 
ggplot(data = inter_zonal_flow,
       aes(x = log(dist),
           y = log(MORNING_PEAK))) +
  geom_point() +
  geom_smooth(method = lm)

9.3 Correlation Analysis

Before I proceed to do SIM, I will determine if there are any correlations between the variables. Conducting a correlation analysis is vital as it reveals linear relationships between variables, aiding in the identification of associations. This process helps avoid multicollinearity issues, optimizing regression models by selecting pertinent variables.

Code 
inter_zonal_flow$BUSINESS_num <- as.numeric(inter_zonal_flow$BUSINESS_num)

inter_zonal_flow$FB_num<- as.numeric(inter_zonal_flow$FB_num)

inter_zonal_flow$lr_num <- as.numeric(inter_zonal_flow$lr_num)

inter_zonal_flow$schools_num <- as.numeric(inter_zonal_flow$schools_num)

inter_zonal_flow$hdb_num <- as.numeric(inter_zonal_flow$hdb_num)

inter_zonal_flow$entertn_num <- as.numeric(inter_zonal_flow$entertn_num)

inter_zonal_flow$MORNING_PEAK<- as.numeric(inter_zonal_flow$MORNING_PEAK)

Now, we draw the correlation matrix:

Code 
vars.cor <- cor(inter_zonal_flow[, 3:9])

corrplot(
  vars.cor,
  method = "ellipse",
  lower = "ellipse",
  upper = "number",
  tl.pos = "lt",
  diag = FALSE, 
  addCoef.col = "black",
  tl.col = "black",
  col = colorRampPalette(c("yellow", "white", "red"))(100) ,number.cex = 0.7
)

The correlation analysis revealed a notable relationship between the variables “F&B” and “Leisure & Recreation” with a correlation coefficient exceeding 80%. This high correlation suggests a strong linear association between the two variables. As a result, it is advisable to retain only one of them in subsequent analyses to avoid issues of multicol-linearity.

Therefore, we choose to remove “Leisure & Recreation” and remain “F&B”. The following table is new explanatory variables to be used in the Spatial Interaction Modelling:

No Explanatory Variables
1 Business
2 F&B
3 schools
4 HDB
5 Entertainment

9.4 Calibrating Spatial Interaction Models

9.4.1 Unconstrained Spatial Interaction Model

Unconstrained SIM

The code chunk used to calibrate to model is shown below:

Code 
uncSIM <- glm(formula = MORNING_PEAK ~ 
                log(BUSINESS_num) +
                log(FB_num) +
                log(schools_num) +
                log(hdb_num) +
                log(entertn_num)+
                log(dist),
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
R-squared

the calculated R-squared is 0.12527437, indicating that the model accounts for approximately 12.53% of the variability in the observed MORNING_PEAK.

Code 
CalcRSquared <- function(observed,estimated){
  r <- cor(observed,estimated)
  R2 <- r^2
  R2
}

CalcRSquared(uncSIM$data$MORNING_PEAK, uncSIM$fitted.values)
[1] 0.1247437
Coefficients
Code 
uncSIM$coefficients
      (Intercept) log(BUSINESS_num)       log(FB_num)  log(schools_num) 
      16.67686922        0.05927062        0.03310465        0.21753349 
     log(hdb_num)  log(entertn_num)         log(dist) 
       0.20942559        0.22414936       -1.41229192
Summary
Code 
summary(uncSIM)

Call:
glm(formula = MORNING_PEAK ~ log(BUSINESS_num) + log(FB_num) + 
    log(schools_num) + log(hdb_num) + log(entertn_num) + log(dist), 
    family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                    Estimate Std. Error z value Pr(>|z|)    
(Intercept)       16.6768692  0.0019208  8682.0   <2e-16 ***
log(BUSINESS_num)  0.0592706  0.0001788   331.4   <2e-16 ***
log(FB_num)        0.0331046  0.0002402   137.8   <2e-16 ***
log(schools_num)   0.2175335  0.0006458   336.9   <2e-16 ***
log(hdb_num)       0.2094256  0.0001380  1517.7   <2e-16 ***
log(entertn_num)   0.2241494  0.0007501   298.8   <2e-16 ***
log(dist)         -1.4122919  0.0002495 -5661.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 101244825  on 64961  degrees of freedom
Residual deviance:  62792208  on 64955  degrees of freedom
AIC: 63150592

Number of Fisher Scoring iterations: 7

9.4.2 Origin Constrained Model

Origin Constrained SIM

Code chunk below shows the calibration of the model by using glm() of R and flow_data.

Code 
orcSIM <- glm(formula = MORNING_PEAK ~ 
                ORIGIN_SZ +
                log(BUSINESS_num) +
                log(FB_num) +
                
                log(schools_num) +
                log(hdb_num) +
                log(entertn_num)+
                log(dist) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
R-squared

the calculated R-squared is 0.2402228, indicating that the model accounts for approximately 24.02% of the variability in the observed MORNING_PEAK.

Code 
CalcRSquared(orcSIM$data$MORNING_PEAK, orcSIM$fitted.values)
[1] 0.2402228
Coefficients
Code 
orcSIM$coefficients[818:823]
log(BUSINESS_num)       log(FB_num)  log(schools_num)      log(hdb_num) 
        0.1145699         0.1319546         0.1776087         0.1227611 
 log(entertn_num)         log(dist) 
        0.2532727        -1.4416487
Summary
Code 
summary(orcSIM)

Call:
glm(formula = MORNING_PEAK ~ ORIGIN_SZ + log(BUSINESS_num) + 
    log(FB_num) + log(schools_num) + log(hdb_num) + log(entertn_num) + 
    log(dist) - 1, family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                    Estimate Std. Error   z value Pr(>|z|)    
ORIGIN_SZ23       13.6371930  0.1270169   107.365   <2e-16 ***
ORIGIN_SZ44       14.3998717  0.1414392   101.810   <2e-16 ***
ORIGIN_SZ46       12.7403468  0.0924677   137.782   <2e-16 ***
ORIGIN_SZ66       13.5383719  0.1302054   103.977   <2e-16 ***
ORIGIN_SZ67       14.7573273  0.0259747   568.142   <2e-16 ***
ORIGIN_SZ68       12.8086473  0.1104479   115.970   <2e-16 ***
ORIGIN_SZ86       13.6730129  0.0803349   170.200   <2e-16 ***
ORIGIN_SZ87       15.3667022  0.0739574   207.778   <2e-16 ***
ORIGIN_SZ88       15.5861467  0.0189635   821.902   <2e-16 ***
ORIGIN_SZ89       13.5665982  0.0496043   273.497   <2e-16 ***
ORIGIN_SZ90       12.9063595  0.1231060   104.839   <2e-16 ***
ORIGIN_SZ109      13.5231995  0.0894638   151.158   <2e-16 ***
ORIGIN_SZ110      13.7067486  0.0762736   179.705   <2e-16 ***
ORIGIN_SZ111      16.5576703  0.0114502  1446.065   <2e-16 ***
ORIGIN_SZ112      12.8861335  0.0685468   187.990   <2e-16 ***
ORIGIN_SZ128      16.1234129  0.0232791   692.612   <2e-16 ***
ORIGIN_SZ129      13.1831647  0.1767892    74.570   <2e-16 ***
ORIGIN_SZ130      14.1769985  0.0527377   268.821   <2e-16 ***
ORIGIN_SZ131      14.4127053  0.0316185   455.831   <2e-16 ***
ORIGIN_SZ132      13.2849004  0.0532608   249.431   <2e-16 ***
ORIGIN_SZ133      13.5237671  0.0408696   330.900   <2e-16 ***
ORIGIN_SZ134      15.8966693  0.0242145   656.493   <2e-16 ***
ORIGIN_SZ150      16.2978631  0.0198543   820.871   <2e-16 ***
ORIGIN_SZ151      13.3718598  0.0662482   201.845   <2e-16 ***
ORIGIN_SZ152      12.6979398  0.0824984   153.917   <2e-16 ***
ORIGIN_SZ153      14.0984175  0.0420025   335.656   <2e-16 ***
ORIGIN_SZ154      16.6825926  0.0090750  1838.297   <2e-16 ***
ORIGIN_SZ155      13.5966151  0.0355186   382.802   <2e-16 ***
ORIGIN_SZ156      14.4620608  0.0435180   332.324   <2e-16 ***
ORIGIN_SZ172      14.9911064  0.0639192   234.532   <2e-16 ***
ORIGIN_SZ174      13.9885171  0.0470199   297.502   <2e-16 ***
ORIGIN_SZ175      16.0977944  0.0103197  1559.915   <2e-16 ***
ORIGIN_SZ176      17.2536974  0.0062502  2760.506   <2e-16 ***
ORIGIN_SZ195      13.0764242  0.0781080   167.415   <2e-16 ***
ORIGIN_SZ196      13.6161083  0.0386532   352.263   <2e-16 ***
ORIGIN_SZ197      12.5024177  0.1240488   100.786   <2e-16 ***
ORIGIN_SZ215      13.9064176  0.0864108   160.934   <2e-16 ***
ORIGIN_SZ216      17.5183224  0.0053407  3280.184   <2e-16 ***
ORIGIN_SZ217      14.8690446  0.0212652   699.221   <2e-16 ***
ORIGIN_SZ237      12.5225365  0.1666773    75.130   <2e-16 ***
ORIGIN_SZ238      13.2478875  0.0712749   185.870   <2e-16 ***
ORIGIN_SZ239      13.5878274  0.1360979    99.839   <2e-16 ***
ORIGIN_SZ257      13.5014239  0.0577665   233.724   <2e-16 ***
ORIGIN_SZ258      14.4462515  0.0285670   505.696   <2e-16 ***
ORIGIN_SZ259      14.2502358  0.0396690   359.228   <2e-16 ***
ORIGIN_SZ278      15.2806884  0.0346581   440.899   <2e-16 ***
ORIGIN_SZ279      13.2379013  0.0441496   299.842   <2e-16 ***
ORIGIN_SZ280      13.6300652  0.0479320   284.363   <2e-16 ***
ORIGIN_SZ298      10.8564638  0.3333387    32.569   <2e-16 ***
ORIGIN_SZ299      13.3702118  0.0523537   255.382   <2e-16 ***
ORIGIN_SZ300      16.5175377  0.0085691  1927.569   <2e-16 ***
ORIGIN_SZ320      13.8490521  0.0489461   282.945   <2e-16 ***
ORIGIN_SZ321      13.8203889  0.0747682   184.843   <2e-16 ***
ORIGIN_SZ322      14.7251265  0.0400786   367.406   <2e-16 ***
ORIGIN_SZ340      15.1031677  0.0271520   556.245   <2e-16 ***
ORIGIN_SZ341      13.6159022  0.0449413   302.971   <2e-16 ***
ORIGIN_SZ342      14.3919596  0.0401117   358.797   <2e-16 ***
ORIGIN_SZ363      15.1936277  0.0371860   408.585   <2e-16 ***
ORIGIN_SZ364      14.9481077  0.0265721   562.548   <2e-16 ***
ORIGIN_SZ383      14.4593095  0.0306462   471.813   <2e-16 ***
ORIGIN_SZ384      13.3345107  0.0488324   273.067   <2e-16 ***
ORIGIN_SZ385      14.6340720  0.0465590   314.313   <2e-16 ***
ORIGIN_SZ404      15.3464320  0.0290339   528.569   <2e-16 ***
ORIGIN_SZ405      14.1098214  0.0514680   274.148   <2e-16 ***
ORIGIN_SZ406      18.4385147  0.0030793  5987.858   <2e-16 ***
ORIGIN_SZ407      14.9931251  0.0390034   384.405   <2e-16 ***
ORIGIN_SZ408      15.6956577  0.0197654   794.099   <2e-16 ***
ORIGIN_SZ425      12.6447000  0.0966917   130.773   <2e-16 ***
ORIGIN_SZ426      14.4895031  0.0302644   478.763   <2e-16 ***
ORIGIN_SZ427      13.3984445  0.0423405   316.445   <2e-16 ***
ORIGIN_SZ428      13.6274613  0.0739488   184.282   <2e-16 ***
ORIGIN_SZ429      16.1986156  0.0173204   935.232   <2e-16 ***
ORIGIN_SZ446      14.1674529  0.0583537   242.786   <2e-16 ***
ORIGIN_SZ447      13.7207898  0.0402379   340.991   <2e-16 ***
ORIGIN_SZ448      14.5657430  0.0270316   538.842   <2e-16 ***
ORIGIN_SZ449      17.3659003  0.0062471  2779.836   <2e-16 ***
ORIGIN_SZ450      15.5758092  0.0174042   894.948   <2e-16 ***
ORIGIN_SZ468      14.6220318  0.0306029   477.798   <2e-16 ***
ORIGIN_SZ469      15.4969625  0.0151304  1024.228   <2e-16 ***
ORIGIN_SZ470      17.8317688  0.0046273  3853.623   <2e-16 ***
ORIGIN_SZ471      16.3895329  0.0146396  1119.533   <2e-16 ***
ORIGIN_SZ488      14.2719675  0.0553340   257.924   <2e-16 ***
ORIGIN_SZ489      11.7898296  0.1601388    73.623   <2e-16 ***
ORIGIN_SZ490      16.0200378  0.0123690  1295.177   <2e-16 ***
ORIGIN_SZ491      16.5599799  0.0077078  2148.476   <2e-16 ***
ORIGIN_SZ493      11.6084215  0.1690415    68.672   <2e-16 ***
ORIGIN_SZ494      13.6638105  0.0626515   218.092   <2e-16 ***
ORIGIN_SZ509      14.2544412  0.0365823   389.654   <2e-16 ***
ORIGIN_SZ510      14.8590608  0.0252682   588.055   <2e-16 ***
ORIGIN_SZ511      15.6890545  0.0110488  1419.978   <2e-16 ***
ORIGIN_SZ512      18.2483529  0.0034565  5279.402   <2e-16 ***
ORIGIN_SZ513      14.9710746  0.0244058   613.422   <2e-16 ***
ORIGIN_SZ514      14.2955817  0.0388243   368.213   <2e-16 ***
ORIGIN_SZ515      12.0129762  0.1525101    78.768   <2e-16 ***
ORIGIN_SZ530      13.5662242  0.0870589   155.828   <2e-16 ***
ORIGIN_SZ531      14.8866777  0.0193348   769.944   <2e-16 ***
ORIGIN_SZ532      14.1788122  0.0252809   560.851   <2e-16 ***
ORIGIN_SZ533      18.1101815  0.0034565  5239.399   <2e-16 ***
ORIGIN_SZ534      18.3426395  0.0037958  4832.369   <2e-16 ***
ORIGIN_SZ536      14.9570996  0.0252874   591.485   <2e-16 ***
ORIGIN_SZ537      12.6594397  0.1221845   103.609   <2e-16 ***
ORIGIN_SZ538      12.9636969  0.2085257    62.168   <2e-16 ***
ORIGIN_SZ539      11.7682512  1.0000024    11.768   <2e-16 ***
ORIGIN_SZ551      13.6201379  0.0530872   256.561   <2e-16 ***
ORIGIN_SZ552      15.6980843  0.0361772   433.921   <2e-16 ***
ORIGIN_SZ553      14.7751096  0.0174875   844.894   <2e-16 ***
ORIGIN_SZ554      18.0270233  0.0037604  4793.855   <2e-16 ***
ORIGIN_SZ555      17.4175108  0.0069378  2510.514   <2e-16 ***
ORIGIN_SZ559      13.4044730  0.0976085   137.329   <2e-16 ***
ORIGIN_SZ560      15.5654515  0.0450009   345.892   <2e-16 ***
ORIGIN_SZ561       9.4248423  1.0000015     9.425   <2e-16 ***
ORIGIN_SZ572      10.6932892  0.4082524    26.193   <2e-16 ***
ORIGIN_SZ573      13.8999804  0.0419978   330.969   <2e-16 ***
ORIGIN_SZ574      14.8602990  0.0368346   403.433   <2e-16 ***
ORIGIN_SZ575      18.8258723  0.0025888  7272.166   <2e-16 ***
ORIGIN_SZ576      17.4929353  0.0049323  3546.622   <2e-16 ***
ORIGIN_SZ578      12.7145754  0.0976084   130.261   <2e-16 ***
ORIGIN_SZ582      13.0664380  0.1048447   124.627   <2e-16 ***
ORIGIN_SZ583      12.8770345  0.4082548    31.542   <2e-16 ***
ORIGIN_SZ584      15.6344658  0.0514784   303.709   <2e-16 ***
ORIGIN_SZ593      14.0990971  0.0482095   292.455   <2e-16 ***
ORIGIN_SZ594      15.0264706  0.0252806   594.387   <2e-16 ***
ORIGIN_SZ595      14.5664960  0.0188263   773.731   <2e-16 ***
ORIGIN_SZ596      17.3914121  0.0043625  3986.534   <2e-16 ***
ORIGIN_SZ597      13.9937538  0.0573885   243.842   <2e-16 ***
ORIGIN_SZ603      13.2842312  0.1097807   121.007   <2e-16 ***
ORIGIN_SZ604      13.9890671  0.1825893    76.615   <2e-16 ***
ORIGIN_SZ615      13.2733065  0.0459705   288.735   <2e-16 ***
ORIGIN_SZ616      14.1815503  0.0313998   451.644   <2e-16 ***
ORIGIN_SZ617      15.0887684  0.0181672   830.548   <2e-16 ***
ORIGIN_SZ618      17.8726200  0.0038927  4591.345   <2e-16 ***
ORIGIN_SZ620      14.6951703  0.0298798   491.810   <2e-16 ***
ORIGIN_SZ637      13.7311618  0.0414944   330.916   <2e-16 ***
ORIGIN_SZ638      17.4594446  0.0042411  4116.696   <2e-16 ***
ORIGIN_SZ657      15.3266460  0.0164622   931.018   <2e-16 ***
ORIGIN_SZ658      16.6465542  0.0063674  2614.324   <2e-16 ***
ORIGIN_SZ659      17.0727059  0.0054192  3150.409   <2e-16 ***
ORIGIN_SZ660      18.0546541  0.0034751  5195.497   <2e-16 ***
ORIGIN_SZ662      17.6795684  0.0070293  2515.114   <2e-16 ***
ORIGIN_SZ677      15.3085069  0.0225131   679.981   <2e-16 ***
ORIGIN_SZ678      13.1730119  0.0465651   282.894   <2e-16 ***
ORIGIN_SZ679      17.8361654  0.0037366  4773.385   <2e-16 ***
ORIGIN_SZ680      17.8861785  0.0037006  4833.329   <2e-16 ***
ORIGIN_SZ681      17.0974098  0.0082779  2065.437   <2e-16 ***
ORIGIN_SZ699      14.8049075  0.0224525   659.387   <2e-16 ***
ORIGIN_SZ700      16.8448335  0.0060781  2771.419   <2e-16 ***
ORIGIN_SZ701      17.0874053  0.0060985  2801.893   <2e-16 ***
ORIGIN_SZ702      17.8904517  0.0036723  4871.694   <2e-16 ***
ORIGIN_SZ704      14.6423770  0.0318113   460.289   <2e-16 ***
ORIGIN_SZ722      15.0971464  0.0182973   825.100   <2e-16 ***
ORIGIN_SZ725      14.1390478  0.0403717   350.221   <2e-16 ***
ORIGIN_SZ741      15.3717380  0.0163132   942.288   <2e-16 ***
ORIGIN_SZ743      15.4104237  0.0123741  1245.373   <2e-16 ***
ORIGIN_SZ744      17.4075162  0.0045911  3791.592   <2e-16 ***
ORIGIN_SZ761      14.9755110  0.0276262   542.077   <2e-16 ***
ORIGIN_SZ762      16.9138856  0.0071539  2364.289   <2e-16 ***
ORIGIN_SZ763      13.9949136  0.0268781   520.681   <2e-16 ***
ORIGIN_SZ764      17.7357820  0.0035970  4930.684   <2e-16 ***
ORIGIN_SZ765      17.1650783  0.0082780  2073.580   <2e-16 ***
ORIGIN_SZ767      18.4189935  0.0038082  4836.676   <2e-16 ***
ORIGIN_SZ772      13.2126349  0.0743554   177.696   <2e-16 ***
ORIGIN_SZ784      13.9607428  0.0265350   526.126   <2e-16 ***
ORIGIN_SZ785      17.0670025  0.0044596  3827.033   <2e-16 ***
ORIGIN_SZ786      16.5649178  0.0061046  2713.529   <2e-16 ***
ORIGIN_SZ787      17.1908544  0.0072233  2379.925   <2e-16 ***
ORIGIN_SZ788      17.7502995  0.0053234  3334.414   <2e-16 ***
ORIGIN_SZ789      16.6504584  0.0102988  1616.741   <2e-16 ***
ORIGIN_SZ803      13.2713650  0.0530349   250.238   <2e-16 ***
ORIGIN_SZ804      17.8525192  0.0042235  4226.995   <2e-16 ***
ORIGIN_SZ805      17.6333880  0.0036250  4864.383   <2e-16 ***
ORIGIN_SZ806      17.2991957  0.0043960  3935.206   <2e-16 ***
ORIGIN_SZ807      18.1058259  0.0042935  4217.058   <2e-16 ***
ORIGIN_SZ808      16.3953247  0.0108686  1508.505   <2e-16 ***
ORIGIN_SZ809      18.0342351  0.0036208  4980.785   <2e-16 ***
ORIGIN_SZ810      17.7054029  0.0056553  3130.738   <2e-16 ***
ORIGIN_SZ814      14.8119714  0.0266605   555.577   <2e-16 ***
ORIGIN_SZ819      19.3294862  0.0173205  1115.986   <2e-16 ***
ORIGIN_SZ824      14.2455165  0.0380635   374.257   <2e-16 ***
ORIGIN_SZ826      15.4797766  0.0099712  1552.441   <2e-16 ***
ORIGIN_SZ827      17.5706855  0.0039825  4411.971   <2e-16 ***
ORIGIN_SZ828      17.5499238  0.0038700  4534.868   <2e-16 ***
ORIGIN_SZ829      17.7009087  0.0046123  3837.781   <2e-16 ***
ORIGIN_SZ830      17.7134562  0.0050901  3479.957   <2e-16 ***
ORIGIN_SZ831      18.3203797  0.0031379  5838.510   <2e-16 ***
ORIGIN_SZ832      17.5766317  0.0060303  2914.721   <2e-16 ***
ORIGIN_SZ835      14.8318746  0.0286578   517.552   <2e-16 ***
ORIGIN_SZ844      13.2377980  0.0741515   178.524   <2e-16 ***
ORIGIN_SZ846      16.9724733  0.0053483  3173.445   <2e-16 ***
ORIGIN_SZ847      15.9800068  0.0090625  1763.305   <2e-16 ***
ORIGIN_SZ848      17.1110257  0.0048783  3507.602   <2e-16 ***
ORIGIN_SZ849      16.2586270  0.0076302  2130.829   <2e-16 ***
ORIGIN_SZ850      17.0213712  0.0054835  3104.090   <2e-16 ***
ORIGIN_SZ851      17.5785225  0.0042340  4151.722   <2e-16 ***
ORIGIN_SZ852      17.2742105  0.0060313  2864.093   <2e-16 ***
ORIGIN_SZ853      19.2389259  0.0037278  5160.939   <2e-16 ***
ORIGIN_SZ854      15.0017024  0.0252145   594.962   <2e-16 ***
ORIGIN_SZ855      13.9013801  0.0430339   323.033   <2e-16 ***
ORIGIN_SZ856      15.3862908  0.0181233   848.976   <2e-16 ***
ORIGIN_SZ866      14.9281528  0.0266072   561.056   <2e-16 ***
ORIGIN_SZ867      15.7466425  0.0116342  1353.475   <2e-16 ***
ORIGIN_SZ868      15.0710856  0.0175774   857.412   <2e-16 ***
ORIGIN_SZ869      17.6655547  0.0059891  2949.640   <2e-16 ***
ORIGIN_SZ870      17.9894473  0.0031919  5635.946   <2e-16 ***
ORIGIN_SZ871      17.4912169  0.0056735  3082.941   <2e-16 ***
ORIGIN_SZ872      15.6964057  0.0110250  1423.710   <2e-16 ***
ORIGIN_SZ873      16.2263022  0.0098449  1648.193   <2e-16 ***
ORIGIN_SZ874      16.3633059  0.0078839  2075.535   <2e-16 ***
ORIGIN_SZ875      13.2263330  0.0649850   203.529   <2e-16 ***
ORIGIN_SZ876      14.3211345  0.0301697   474.686   <2e-16 ***
ORIGIN_SZ877      13.7215617  0.0389380   352.396   <2e-16 ***
ORIGIN_SZ887      15.3800244  0.0131646  1168.288   <2e-16 ***
ORIGIN_SZ888      16.7541544  0.0068828  2434.196   <2e-16 ***
ORIGIN_SZ889      13.9707130  0.0311131   449.031   <2e-16 ***
ORIGIN_SZ890      17.6736621  0.0038271  4617.999   <2e-16 ***
ORIGIN_SZ891      16.7746864  0.0109459  1532.502   <2e-16 ***
ORIGIN_SZ893      17.5985296  0.0040879  4305.069   <2e-16 ***
ORIGIN_SZ894      15.8470957  0.0103608  1529.521   <2e-16 ***
ORIGIN_SZ895      15.3861702  0.0149665  1028.044   <2e-16 ***
ORIGIN_SZ896      14.5807779  0.0289360   503.898   <2e-16 ***
ORIGIN_SZ897      12.9424322  0.0608868   212.565   <2e-16 ***
ORIGIN_SZ898      14.5951677  0.0309920   470.934   <2e-16 ***
ORIGIN_SZ908      16.5864777  0.0118096  1404.494   <2e-16 ***
ORIGIN_SZ909      16.8259457  0.0056513  2977.343   <2e-16 ***
ORIGIN_SZ910      14.8991599  0.0162636   916.104   <2e-16 ***
ORIGIN_SZ911      16.1698529  0.0086363  1872.316   <2e-16 ***
ORIGIN_SZ912      17.3790211  0.0043210  4022.014   <2e-16 ***
ORIGIN_SZ915      17.5858671  0.0043692  4024.942   <2e-16 ***
ORIGIN_SZ917      16.9766226  0.0071239  2383.059   <2e-16 ***
ORIGIN_SZ918      13.5562937  0.0381183   355.638   <2e-16 ***
ORIGIN_SZ919      16.5729445  0.0090950  1822.196   <2e-16 ***
ORIGIN_SZ928      15.9211622  0.0129943  1225.240   <2e-16 ***
ORIGIN_SZ929      17.2839509  0.0045412  3806.021   <2e-16 ***
ORIGIN_SZ930      17.9335099  0.0032500  5518.036   <2e-16 ***
ORIGIN_SZ931      14.9537314  0.0165995   900.854   <2e-16 ***
ORIGIN_SZ932      15.5329896  0.0173966   892.876   <2e-16 ***
ORIGIN_SZ933      17.1852612  0.0055670  3086.967   <2e-16 ***
ORIGIN_SZ934      14.6448385  0.0189045   774.673   <2e-16 ***
ORIGIN_SZ935      18.1361001  0.0032278  5618.799   <2e-16 ***
ORIGIN_SZ938      11.3262623  0.2500064    45.304   <2e-16 ***
ORIGIN_SZ939      18.2203410  0.0038382  4747.112   <2e-16 ***
ORIGIN_SZ940      13.4542375  0.0707351   190.206   <2e-16 ***
ORIGIN_SZ949      15.5500869  0.0128918  1206.204   <2e-16 ***
ORIGIN_SZ950      17.5448610  0.0048540  3614.515   <2e-16 ***
ORIGIN_SZ951      18.3263309  0.0029195  6277.218   <2e-16 ***
ORIGIN_SZ952      15.4810011  0.0199869   774.556   <2e-16 ***
ORIGIN_SZ953      16.2868574  0.0092849  1754.117   <2e-16 ***
ORIGIN_SZ954      14.7757276  0.0164872   896.192   <2e-16 ***
ORIGIN_SZ955      16.9560761  0.0056181  3018.135   <2e-16 ***
ORIGIN_SZ956      15.5897678  0.0112334  1387.807   <2e-16 ***
ORIGIN_SZ957      17.5949922  0.0055287  3182.462   <2e-16 ***
ORIGIN_SZ959      14.2206827  0.0475470   299.087   <2e-16 ***
ORIGIN_SZ961      14.2766045  0.0300752   474.697   <2e-16 ***
ORIGIN_SZ962      20.8976545  0.0043068  4852.282   <2e-16 ***
ORIGIN_SZ970      16.2227070  0.0078012  2079.518   <2e-16 ***
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ORIGIN_SZ2086     17.6215580  0.0039714  4437.060   <2e-16 ***
ORIGIN_SZ2087     16.3950722  0.0068826  2382.112   <2e-16 ***
ORIGIN_SZ2088     17.0908524  0.0045294  3773.308   <2e-16 ***
ORIGIN_SZ2089     16.8675590  0.0062539  2697.132   <2e-16 ***
ORIGIN_SZ2090     17.8315057  0.0034963  5100.146   <2e-16 ***
ORIGIN_SZ2091     13.6955859  0.0631468   216.885   <2e-16 ***
ORIGIN_SZ2105     14.1125812  0.0985581   143.190   <2e-16 ***
ORIGIN_SZ2106     14.6414654  0.0184780   792.373   <2e-16 ***
ORIGIN_SZ2107     15.8314290  0.0086402  1832.308   <2e-16 ***
ORIGIN_SZ2108     17.0084994  0.0053738  3165.070   <2e-16 ***
ORIGIN_SZ2109     17.2431047  0.0044610  3865.294   <2e-16 ***
ORIGIN_SZ2110     16.7916912  0.0071236  2357.179   <2e-16 ***
ORIGIN_SZ2111     14.6874255  0.0384227   382.259   <2e-16 ***
ORIGIN_SZ2128     15.6840940  0.0134195  1168.751   <2e-16 ***
ORIGIN_SZ2129     15.0891198  0.0146034  1033.258   <2e-16 ***
ORIGIN_SZ2130     17.4880134  0.0038775  4510.177   <2e-16 ***
ORIGIN_SZ2131     17.7697711  0.0043766  4060.181   <2e-16 ***
ORIGIN_SZ2132     16.9092159  0.0058602  2885.430   <2e-16 ***
ORIGIN_SZ2148     16.3905292  0.0109595  1495.556   <2e-16 ***
ORIGIN_SZ2149     15.2995992  0.0145826  1049.169   <2e-16 ***
ORIGIN_SZ2150     17.5091513  0.0044395  3943.917   <2e-16 ***
ORIGIN_SZ2151     17.7314741  0.0035096  5052.291   <2e-16 ***
ORIGIN_SZ2152     17.9129001  0.0037585  4765.994   <2e-16 ***
ORIGIN_SZ2153     17.3432375  0.0053764  3225.829   <2e-16 ***
ORIGIN_SZ2171     16.4568918  0.0068831  2390.905   <2e-16 ***
ORIGIN_SZ2172     16.6154908  0.0075332  2205.632   <2e-16 ***
ORIGIN_SZ2173     16.9974571  0.0050314  3378.252   <2e-16 ***
ORIGIN_SZ2174     17.2830673  0.0051222  3374.153   <2e-16 ***
ORIGIN_SZ2191     16.2413756  0.0097908  1658.837   <2e-16 ***
ORIGIN_SZ2192     15.8054056  0.0106206  1488.190   <2e-16 ***
ORIGIN_SZ2193     16.8469406  0.0058486  2880.520   <2e-16 ***
ORIGIN_SZ2194     17.0847071  0.0050136  3407.670   <2e-16 ***
ORIGIN_SZ2195     16.5157113  0.0199754   826.803   <2e-16 ***
ORIGIN_SZ2212     14.0634543  0.0825044   170.457   <2e-16 ***
ORIGIN_SZ2213     14.0099431  0.0361596   387.447   <2e-16 ***
ORIGIN_SZ2214     14.8668683  0.0261041   569.523   <2e-16 ***
ORIGIN_SZ2215     16.7813055  0.0064734  2592.339   <2e-16 ***
ORIGIN_SZ2216     15.8040514  0.0106287  1486.925   <2e-16 ***
ORIGIN_SZ2233     14.1499603  0.0438945   322.363   <2e-16 ***
ORIGIN_SZ2234     16.3120143  0.0191588   851.412   <2e-16 ***
ORIGIN_SZ2235     15.8017816  0.0123113  1283.516   <2e-16 ***
ORIGIN_SZ2236     15.6094875  0.0125479  1243.990   <2e-16 ***
ORIGIN_SZ2237     13.3065457  0.0559328   237.902   <2e-16 ***
ORIGIN_SZ2256     14.2009275  0.0418181   339.588   <2e-16 ***
ORIGIN_SZ2257     15.2607057  0.0188763   808.459   <2e-16 ***
ORIGIN_SZ2258     14.8781858  0.0154325   964.084   <2e-16 ***
ORIGIN_SZ2259     14.5573336  0.0330605   440.324   <2e-16 ***
ORIGIN_SZ2277     15.2450083  0.0366627   415.818   <2e-16 ***
ORIGIN_SZ2278     16.2711543  0.0113003  1439.893   <2e-16 ***
ORIGIN_SZ2279     14.6778939  0.0195616   750.342   <2e-16 ***
ORIGIN_SZ2280     12.6841698  0.1031584   122.958   <2e-16 ***
ORIGIN_SZ2297     17.2675039  0.0088944  1941.382   <2e-16 ***
ORIGIN_SZ2300     13.1130468  0.0674481   194.417   <2e-16 ***
ORIGIN_SZ2301     14.8744683  0.0182382   815.568   <2e-16 ***
ORIGIN_SZ2318     15.6275373  0.0179566   870.293   <2e-16 ***
ORIGIN_SZ2319     16.6558082  0.0099014  1682.170   <2e-16 ***
ORIGIN_SZ2322     16.1067660  0.0112754  1428.491   <2e-16 ***
ORIGIN_SZ2337     17.2852700  0.0146577  1179.264   <2e-16 ***
ORIGIN_SZ2341     16.9876357  0.0088480  1919.947   <2e-16 ***
ORIGIN_SZ2343     15.6464859  0.0135032  1158.721   <2e-16 ***
ORIGIN_SZ2361     16.6635165  0.0112716  1478.363   <2e-16 ***
ORIGIN_SZ2364     12.9334479  0.0733497   176.326   <2e-16 ***
ORIGIN_SZ2379     17.1237880  0.0162800  1051.832   <2e-16 ***
ORIGIN_SZ2384     16.2321989  0.0143144  1133.975   <2e-16 ***
ORIGIN_SZ2405     15.9593360  0.0143219  1114.335   <2e-16 ***
ORIGIN_SZ2406     14.5887345  0.0323372   451.144   <2e-16 ***
ORIGIN_SZ2426     16.3970030  0.0256370   639.583   <2e-16 ***
ORIGIN_SZ2427     16.9094915  0.0104303  1621.196   <2e-16 ***
ORIGIN_SZ2505     16.6423985  0.0384692   432.616   <2e-16 ***
log(BUSINESS_num)  0.1145699  0.0001897   604.087   <2e-16 ***
log(FB_num)        0.1319546  0.0002589   509.608   <2e-16 ***
log(schools_num)   0.1776087  0.0006586   269.689   <2e-16 ***
log(hdb_num)       0.1227611  0.0001474   832.701   <2e-16 ***
log(entertn_num)   0.2532727  0.0007717   328.190   <2e-16 ***
log(dist)         -1.4416487  0.0002609 -5526.339   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 349181331  on 64962  degrees of freedom
Residual deviance:  42866101  on 64139  degrees of freedom
AIC: 43226117

Number of Fisher Scoring iterations: 7

9.4.3 Destin Constrained Model

Destin Constrained SIM

The code chunk used to calibrate to model is shown below is the destination:

Code 
decSIM  <- glm(formula = MORNING_PEAK ~ 
                DESTIN_SZ +
                log(BUSINESS_num) +
                log(FB_num) +
                
                log(schools_num) +
                log(hdb_num) +
                log(entertn_num)+
                log(dist)-1,
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
R-squared

the calculated R-squared is 0.3053515, indicating that the model accounts for approximately 30.54% of the variability in the observed MORNING_PEAK.

Code 
CalcRSquared(decSIM$data$MORNING_PEAK, decSIM$fitted.values)
[1] 0.3053515
Coefficients
Code 
decSIM$coefficients[820:825]
log(BUSINESS_num)       log(FB_num)  log(schools_num)      log(hdb_num) 
               NA                NA                NA                NA 
 log(entertn_num)         log(dist) 
               NA         -1.461883
Summary
Code 
options(max.print = 10000)
summary(decSIM)

Call:
glm(formula = MORNING_PEAK ~ DESTIN_SZ + log(BUSINESS_num) + 
    log(FB_num) + log(schools_num) + log(hdb_num) + log(entertn_num) + 
    log(dist) - 1, family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients: (5 not defined because of singularities)
                    Estimate Std. Error  z value Pr(>|z|)    
DESTIN_SZ23       16.6350037  0.0504877   329.49   <2e-16 ***
DESTIN_SZ44       17.7648906  0.0226652   783.79   <2e-16 ***
DESTIN_SZ46       16.8708169  0.0191462   881.16   <2e-16 ***
DESTIN_SZ66       15.9389708  0.0461679   345.24   <2e-16 ***
DESTIN_SZ67       16.7983647  0.0137218  1224.21   <2e-16 ***
DESTIN_SZ68       16.8163886  0.0193076   870.97   <2e-16 ***
DESTIN_SZ86       16.8940255  0.0344631   490.21   <2e-16 ***
DESTIN_SZ87       13.9580875  0.0836436   166.88   <2e-16 ***
DESTIN_SZ88       16.2107274  0.0171040   947.77   <2e-16 ***
DESTIN_SZ89       16.6972232  0.0199974   834.97   <2e-16 ***
DESTIN_SZ90       12.1872374  0.7071097    17.23   <2e-16 ***
DESTIN_SZ109      15.9090781  0.0240970   660.21   <2e-16 ***
DESTIN_SZ110      13.0822409  0.1005198   130.15   <2e-16 ***
DESTIN_SZ111      16.7511015  0.0118668  1411.60   <2e-16 ***
DESTIN_SZ112      14.9617633  0.0323917   461.90   <2e-16 ***
DESTIN_SZ128      16.6176074  0.0231683   717.25   <2e-16 ***
DESTIN_SZ129      13.5696912  0.1324650   102.44   <2e-16 ***
DESTIN_SZ130      15.9680273  0.0219343   728.00   <2e-16 ***
DESTIN_SZ131      15.4024371  0.0217725   707.43   <2e-16 ***
DESTIN_SZ132      16.6387249  0.0146895  1132.69   <2e-16 ***
DESTIN_SZ133      16.4221307  0.0123079  1334.28   <2e-16 ***
DESTIN_SZ134      16.6149515  0.0115366  1440.19   <2e-16 ***
DESTIN_SZ150      16.0520048  0.0253139   634.12   <2e-16 ***
DESTIN_SZ151      15.7327201  0.0222516   707.04   <2e-16 ***
DESTIN_SZ152      17.1756622  0.0142121  1208.53   <2e-16 ***
DESTIN_SZ153      16.9664862  0.0129691  1308.23   <2e-16 ***
DESTIN_SZ154      15.1305365  0.0271986   556.30   <2e-16 ***
DESTIN_SZ155      15.8372324  0.0184088   860.31   <2e-16 ***
DESTIN_SZ156      16.3358762  0.0196674   830.61   <2e-16 ***
DESTIN_SZ172      14.5845392  0.0430694   338.63   <2e-16 ***
DESTIN_SZ174      16.4021989  0.0143354  1144.18   <2e-16 ***
DESTIN_SZ175      16.5471268  0.0104815  1578.70   <2e-16 ***
DESTIN_SZ176      14.9585939  0.0264885   564.72   <2e-16 ***
DESTIN_SZ195      15.7298146  0.0295692   531.97   <2e-16 ***
DESTIN_SZ196      16.6844551  0.0100408  1661.67   <2e-16 ***
DESTIN_SZ197      13.4886576  0.0751863   179.40   <2e-16 ***
DESTIN_SZ215      16.5514188  0.0290274   570.20   <2e-16 ***
DESTIN_SZ216      15.8626889  0.0152046  1043.28   <2e-16 ***
DESTIN_SZ217      17.2783169  0.0091383  1890.76   <2e-16 ***
DESTIN_SZ237      16.1171510  0.0305242   528.01   <2e-16 ***
DESTIN_SZ238      16.6697988  0.0147529  1129.93   <2e-16 ***
DESTIN_SZ239      15.6539571  0.0301673   518.90   <2e-16 ***
DESTIN_SZ257      16.4832448  0.0154009  1070.28   <2e-16 ***
DESTIN_SZ258      15.9682169  0.0190669   837.48   <2e-16 ***
DESTIN_SZ259      17.1908916  0.0118314  1452.99   <2e-16 ***
DESTIN_SZ278      16.7794448  0.0137832  1217.38   <2e-16 ***
DESTIN_SZ279      16.4807373  0.0130646  1261.48   <2e-16 ***
DESTIN_SZ280      16.8293849  0.0122569  1373.06   <2e-16 ***
DESTIN_SZ298      13.6812668  0.1291111   105.97   <2e-16 ***
DESTIN_SZ299      16.6761994  0.0157800  1056.80   <2e-16 ***
DESTIN_SZ300      15.8888699  0.0167336   949.52   <2e-16 ***
DESTIN_SZ320      17.1120970  0.0137400  1245.42   <2e-16 ***
DESTIN_SZ321      15.8931575  0.0233389   680.97   <2e-16 ***
DESTIN_SZ322      17.9990148  0.0114968  1565.56   <2e-16 ***
DESTIN_SZ340      18.0084556  0.0105046  1714.34   <2e-16 ***
DESTIN_SZ341      16.8407452  0.0119767  1406.13   <2e-16 ***
DESTIN_SZ342      17.8472835  0.0102467  1741.75   <2e-16 ***
DESTIN_SZ363      17.0920934  0.0130186  1312.90   <2e-16 ***
DESTIN_SZ364      18.1472210  0.0076257  2379.75   <2e-16 ***
DESTIN_SZ383      17.1539570  0.0087594  1958.34   <2e-16 ***
DESTIN_SZ384      18.2281528  0.0082303  2214.77   <2e-16 ***
DESTIN_SZ385      17.2050842  0.0145717  1180.72   <2e-16 ***
DESTIN_SZ404      17.8057962  0.0123818  1438.07   <2e-16 ***
DESTIN_SZ405      17.2056191  0.0102264  1682.48   <2e-16 ***
DESTIN_SZ406      17.5162432  0.0051447  3404.71   <2e-16 ***
DESTIN_SZ407      18.8769281  0.0076649  2462.76   <2e-16 ***
DESTIN_SZ408      19.3525187  0.0043373  4461.89   <2e-16 ***
DESTIN_SZ425      15.7913467  0.0243422   648.72   <2e-16 ***
DESTIN_SZ426      17.0046451  0.0100827  1686.52   <2e-16 ***
DESTIN_SZ427      15.0595385  0.0227629   661.58   <2e-16 ***
DESTIN_SZ428      17.4326472  0.0096489  1806.69   <2e-16 ***
DESTIN_SZ429      16.7217277  0.0212361   787.42   <2e-16 ***
DESTIN_SZ446      17.1256672  0.0223256   767.09   <2e-16 ***
DESTIN_SZ447      16.0327727  0.0168113   953.69   <2e-16 ***
DESTIN_SZ448      17.0192011  0.0114702  1483.78   <2e-16 ***
DESTIN_SZ449      17.7883748  0.0069594  2556.02   <2e-16 ***
DESTIN_SZ450      16.9471362  0.0110126  1538.89   <2e-16 ***
DESTIN_SZ468      17.2399857  0.0105525  1633.73   <2e-16 ***
DESTIN_SZ469      17.1924367  0.0083100  2068.88   <2e-16 ***
DESTIN_SZ470      17.5791594  0.0065198  2696.29   <2e-16 ***
DESTIN_SZ471      16.5772156  0.0152953  1083.81   <2e-16 ***
DESTIN_SZ488      16.1865316  0.0217661   743.66   <2e-16 ***
DESTIN_SZ489      14.7212952  0.0457261   321.94   <2e-16 ***
DESTIN_SZ490      17.3463466  0.0084917  2042.74   <2e-16 ***
DESTIN_SZ491      15.9770695  0.0148026  1079.34   <2e-16 ***
DESTIN_SZ493      14.3167122  0.0477080   300.09   <2e-16 ***
DESTIN_SZ494      16.2070130  0.0216343   749.14   <2e-16 ***
DESTIN_SZ509      15.9972914  0.0147449  1084.94   <2e-16 ***
DESTIN_SZ510      17.3356293  0.0096472  1796.97   <2e-16 ***
DESTIN_SZ511      17.2671211  0.0066432  2599.22   <2e-16 ***
DESTIN_SZ512      17.3427742  0.0063618  2726.09   <2e-16 ***
DESTIN_SZ513      17.7464204  0.0072148  2459.71   <2e-16 ***
DESTIN_SZ514      16.9224595  0.0116174  1456.64   <2e-16 ***
DESTIN_SZ515      15.6696805  0.0296989   527.62   <2e-16 ***
DESTIN_SZ530      15.3908524  0.0283953   542.02   <2e-16 ***
DESTIN_SZ531      17.9922198  0.0058826  3058.57   <2e-16 ***
DESTIN_SZ532      16.9617561  0.0087074  1947.97   <2e-16 ***
DESTIN_SZ533      18.9405165  0.0031746  5966.21   <2e-16 ***
DESTIN_SZ534      17.6841769  0.0063900  2767.49   <2e-16 ***
DESTIN_SZ536      15.8542723  0.0175085   905.52   <2e-16 ***
DESTIN_SZ537      15.3354540  0.0333316   460.09   <2e-16 ***
DESTIN_SZ538      15.0159050  0.0426815   351.81   <2e-16 ***
DESTIN_SZ539      14.0001197  0.2500093    56.00   <2e-16 ***
DESTIN_SZ551      16.3176984  0.0173472   940.65   <2e-16 ***
DESTIN_SZ552      18.6362388  0.0103292  1804.23   <2e-16 ***
DESTIN_SZ553      16.9884919  0.0084946  1999.93   <2e-16 ***
DESTIN_SZ554      17.3254481  0.0066826  2592.61   <2e-16 ***
DESTIN_SZ555      17.6793305  0.0073795  2395.72   <2e-16 ***
DESTIN_SZ559      15.6614521  0.0529668   295.68   <2e-16 ***
DESTIN_SZ560      16.9584128  0.0161495  1050.09   <2e-16 ***
DESTIN_SZ561      15.6756427  0.0641880   244.21   <2e-16 ***
DESTIN_SZ572      16.5303733  0.0342533   482.59   <2e-16 ***
DESTIN_SZ573      17.2474249  0.0099580  1732.02   <2e-16 ***
DESTIN_SZ574      17.1383588  0.0154267  1110.95   <2e-16 ***
DESTIN_SZ575      19.4038343  0.0025184  7704.92   <2e-16 ***
DESTIN_SZ576      17.4550171  0.0062076  2811.90   <2e-16 ***
DESTIN_SZ578      13.2867423  0.0976082   136.12   <2e-16 ***
DESTIN_SZ582      14.8272003  0.0612279   242.16   <2e-16 ***
DESTIN_SZ583      13.6634209  0.1825843    74.83   <2e-16 ***
DESTIN_SZ584      16.6164471  0.0343869   483.22   <2e-16 ***
DESTIN_SZ593      15.7980949  0.0249032   634.38   <2e-16 ***
DESTIN_SZ594      16.6145107  0.0133112  1248.16   <2e-16 ***
DESTIN_SZ595      17.6899936  0.0058536  3022.09   <2e-16 ***
DESTIN_SZ596      17.6715881  0.0050997  3465.24   <2e-16 ***
DESTIN_SZ597      17.3190976  0.0149428  1159.03   <2e-16 ***
DESTIN_SZ603      14.7314038  0.0511291   288.12   <2e-16 ***
DESTIN_SZ604      16.9938545  0.0492599   344.98   <2e-16 ***
DESTIN_SZ615      15.9197596  0.0144271  1103.46   <2e-16 ***
DESTIN_SZ616      17.4648127  0.0086819  2011.64   <2e-16 ***
DESTIN_SZ617      16.5733942  0.0090141  1838.61   <2e-16 ***
DESTIN_SZ618      17.4535085  0.0062524  2791.51   <2e-16 ***
DESTIN_SZ620      17.1285449  0.0106657  1605.95   <2e-16 ***
DESTIN_SZ637      16.9761427  0.0107006  1586.47   <2e-16 ***
DESTIN_SZ638      17.4409559  0.0057167  3050.87   <2e-16 ***
DESTIN_SZ657      17.5626225  0.0070019  2508.27   <2e-16 ***
DESTIN_SZ658      17.3208974  0.0060701  2853.49   <2e-16 ***
DESTIN_SZ659      17.6384628  0.0057368  3074.62   <2e-16 ***
DESTIN_SZ660      18.2538855  0.0040861  4467.32   <2e-16 ***
DESTIN_SZ662      16.9808432  0.0115807  1466.31   <2e-16 ***
DESTIN_SZ677      17.7386129  0.0092539  1916.89   <2e-16 ***
DESTIN_SZ678      16.1434356  0.0137714  1172.24   <2e-16 ***
DESTIN_SZ679      17.6987142  0.0049770  3556.13   <2e-16 ***
DESTIN_SZ680      19.5108225  0.0026778  7286.16   <2e-16 ***
DESTIN_SZ681      16.2941696  0.0175510   928.39   <2e-16 ***
DESTIN_SZ699      17.0802411  0.0089024  1918.61   <2e-16 ***
DESTIN_SZ700      17.3754689  0.0068593  2533.14   <2e-16 ***
DESTIN_SZ701      15.3904622  0.0191672   802.96   <2e-16 ***
DESTIN_SZ702      17.8741006  0.0046971  3805.34   <2e-16 ***
DESTIN_SZ704      17.3239918  0.0106139  1632.19   <2e-16 ***
DESTIN_SZ722      17.1982826  0.0087045  1975.80   <2e-16 ***
DESTIN_SZ725      15.6113259  0.0259626   601.30   <2e-16 ***
DESTIN_SZ741      17.6248992  0.0071347  2470.30   <2e-16 ***
DESTIN_SZ743      15.0699990  0.0203173   741.73   <2e-16 ***
DESTIN_SZ744      17.9352949  0.0048603  3690.20   <2e-16 ***
DESTIN_SZ761      17.7189488  0.0082410  2150.09   <2e-16 ***
DESTIN_SZ762      16.0792596  0.0131711  1220.80   <2e-16 ***
DESTIN_SZ763      15.1629935  0.0196043   773.45   <2e-16 ***
DESTIN_SZ764      18.2237883  0.0037249  4892.36   <2e-16 ***
DESTIN_SZ765      17.3932101  0.0095007  1830.74   <2e-16 ***
DESTIN_SZ767      17.6473791  0.0066086  2670.35   <2e-16 ***
DESTIN_SZ772      15.2976079  0.0378704   403.95   <2e-16 ***
DESTIN_SZ784      15.3332579  0.0209105   733.28   <2e-16 ***
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DESTIN_SZ1792     17.4850258  0.0067722  2581.88   <2e-16 ***
DESTIN_SZ1793     17.3294121  0.0056848  3048.36   <2e-16 ***
DESTIN_SZ1794     18.4045864  0.0074073  2484.66   <2e-16 ***
DESTIN_SZ1795     15.3145014  0.0204110   750.30   <2e-16 ***
DESTIN_SZ1796     17.7496309  0.0052356  3390.21   <2e-16 ***
DESTIN_SZ1797     17.4572012  0.0053366  3271.22   <2e-16 ***
DESTIN_SZ1798     17.8062969  0.0051241  3474.98   <2e-16 ***
DESTIN_SZ1799     16.8403725  0.0086635  1943.82   <2e-16 ***
DESTIN_SZ1800     15.1299119  0.0504103   300.13   <2e-16 ***
DESTIN_SZ1811     16.8623634  0.0075259  2240.57   <2e-16 ***
DESTIN_SZ1812     18.2088057  0.0034745  5240.72   <2e-16 ***
DESTIN_SZ1813     18.3473031  0.0034038  5390.28   <2e-16 ***
DESTIN_SZ1817     16.3418479  0.0112903  1447.43   <2e-16 ***
DESTIN_SZ1818     17.3959086  0.0057082  3047.54   <2e-16 ***
DESTIN_SZ1819     19.0301177  0.0029167  6524.44   <2e-16 ***
DESTIN_SZ1820     14.4879397  0.0428302   338.26   <2e-16 ***
DESTIN_SZ1832     18.1721450  0.0042019  4324.70   <2e-16 ***
DESTIN_SZ1833     16.8372061  0.0068755  2448.88   <2e-16 ***
DESTIN_SZ1834     16.8405088  0.0065834  2558.04   <2e-16 ***
DESTIN_SZ1835     16.9110546  0.0074557  2268.19   <2e-16 ***
DESTIN_SZ1837     16.8043957  0.0135585  1239.39   <2e-16 ***
DESTIN_SZ1839     16.2886982  0.0119564  1362.34   <2e-16 ***
DESTIN_SZ1840     18.8848321  0.0032670  5780.55   <2e-16 ***
DESTIN_SZ1841     15.6033295  0.0232972   669.75   <2e-16 ***
DESTIN_SZ1842     16.8940267  0.0145941  1157.59   <2e-16 ***
DESTIN_SZ1853     17.1972783  0.0057046  3014.65   <2e-16 ***
DESTIN_SZ1854     17.4684080  0.0050452  3462.36   <2e-16 ***
DESTIN_SZ1855     17.9040269  0.0045582  3927.88   <2e-16 ***
DESTIN_SZ1858     17.5610522  0.0082326  2133.10   <2e-16 ***
DESTIN_SZ1860     17.0935896  0.0183125   933.44   <2e-16 ***
DESTIN_SZ1861     17.6914934  0.0058028  3048.77   <2e-16 ***
DESTIN_SZ1874     16.8217670  0.0092961  1809.55   <2e-16 ***
DESTIN_SZ1875     15.2454264  0.0202706   752.10   <2e-16 ***
DESTIN_SZ1876     16.3349748  0.0214493   761.56   <2e-16 ***
DESTIN_SZ1877     17.7557939  0.0048933  3628.57   <2e-16 ***
DESTIN_SZ1880     16.5291753  0.0138749  1191.30   <2e-16 ***
DESTIN_SZ1882     17.5795193  0.0061657  2851.16   <2e-16 ***
DESTIN_SZ1883     16.5886458  0.0186349   890.19   <2e-16 ***
DESTIN_SZ1895     17.5350776  0.0051253  3421.30   <2e-16 ***
DESTIN_SZ1896     16.7634577  0.0076140  2201.65   <2e-16 ***
DESTIN_SZ1897     16.3208024  0.0113616  1436.49   <2e-16 ***
DESTIN_SZ1898     15.6552939  0.0247542   632.43   <2e-16 ***
DESTIN_SZ1901     15.9694813  0.0200557   796.26   <2e-16 ***
DESTIN_SZ1903     16.1479844  0.0164380   982.35   <2e-16 ***
DESTIN_SZ1917     16.4402676  0.0088605  1855.45   <2e-16 ***
DESTIN_SZ1918     18.1017515  0.0061984  2920.40   <2e-16 ***
DESTIN_SZ1919     17.9361858  0.0045968  3901.87   <2e-16 ***
DESTIN_SZ1922     17.1134742  0.0105241  1626.13   <2e-16 ***
DESTIN_SZ1924     15.9957806  0.0195998   816.12   <2e-16 ***
DESTIN_SZ1937     16.9263627  0.0074478  2272.66   <2e-16 ***
DESTIN_SZ1938     17.9516126  0.0044855  4002.13   <2e-16 ***
DESTIN_SZ1939     17.0551964  0.0080262  2124.94   <2e-16 ***
DESTIN_SZ1942     16.1549721  0.0186488   866.27   <2e-16 ***
DESTIN_SZ1959     16.6215011  0.0092674  1793.54   <2e-16 ***
DESTIN_SZ1960     19.0879197  0.0026872  7103.25   <2e-16 ***
DESTIN_SZ1961     16.7417291  0.0094841  1765.24   <2e-16 ***
DESTIN_SZ1962     17.5538765  0.0059338  2958.29   <2e-16 ***
DESTIN_SZ1964     18.0694239  0.0109127  1655.82   <2e-16 ***
DESTIN_SZ1979     16.9353751  0.0081770  2071.09   <2e-16 ***
DESTIN_SZ1980     17.0755520  0.0066266  2576.82   <2e-16 ***
DESTIN_SZ1981     17.1623960  0.0069721  2461.56   <2e-16 ***
DESTIN_SZ1982     17.7069090  0.0070717  2503.92   <2e-16 ***
DESTIN_SZ1983     17.5321303  0.0059919  2925.99   <2e-16 ***
DESTIN_SZ1984     17.3040220  0.0061877  2796.50   <2e-16 ***
DESTIN_SZ1985     17.6967797  0.0058128  3044.44   <2e-16 ***
DESTIN_SZ2001     17.0599093  0.0065178  2617.43   <2e-16 ***
DESTIN_SZ2002     17.3903322  0.0050415  3449.47   <2e-16 ***
DESTIN_SZ2003     18.0518300  0.0043596  4140.68   <2e-16 ***
DESTIN_SZ2004     18.3363157  0.0041171  4453.68   <2e-16 ***
DESTIN_SZ2005     17.1532095  0.0063773  2689.73   <2e-16 ***
DESTIN_SZ2006     18.2144546  0.0046465  3920.01   <2e-16 ***
DESTIN_SZ2007     15.0407848  0.0296401   507.45   <2e-16 ***
DESTIN_SZ2022     17.6896037  0.0063981  2764.80   <2e-16 ***
DESTIN_SZ2023     17.8550645  0.0046104  3872.80   <2e-16 ***
DESTIN_SZ2024     18.1751126  0.0039777  4569.24   <2e-16 ***
DESTIN_SZ2025     17.1314917  0.0064363  2661.72   <2e-16 ***
DESTIN_SZ2026     16.3461928  0.0115865  1410.79   <2e-16 ***
DESTIN_SZ2027     18.0907515  0.0044046  4107.22   <2e-16 ***
DESTIN_SZ2043     16.2006762  0.0111394  1454.36   <2e-16 ***
DESTIN_SZ2044     17.2464964  0.0057305  3009.59   <2e-16 ***
DESTIN_SZ2045     16.7799564  0.0116939  1434.93   <2e-16 ***
DESTIN_SZ2046     18.2387337  0.0036676  4972.99   <2e-16 ***
DESTIN_SZ2047     16.5589614  0.0090044  1838.98   <2e-16 ***
DESTIN_SZ2048     16.6440793  0.0084165  1977.57   <2e-16 ***
DESTIN_SZ2049     14.9903280  0.0276919   541.33   <2e-16 ***
DESTIN_SZ2064     17.0500355  0.0069422  2455.99   <2e-16 ***
DESTIN_SZ2065     16.9370135  0.0070668  2396.70   <2e-16 ***
DESTIN_SZ2066     15.1753466  0.0324733   467.32   <2e-16 ***
DESTIN_SZ2067     19.5021151  0.0024554  7942.46   <2e-16 ***
DESTIN_SZ2068     16.6213149  0.0130997  1268.83   <2e-16 ***
DESTIN_SZ2069     16.8594945  0.0082006  2055.89   <2e-16 ***
DESTIN_SZ2085     17.0904490  0.0073605  2321.90   <2e-16 ***
DESTIN_SZ2086     18.2772357  0.0037498  4874.16   <2e-16 ***
DESTIN_SZ2087     18.0889350  0.0040279  4490.89   <2e-16 ***
DESTIN_SZ2088     17.3029530  0.0056087  3085.01   <2e-16 ***
DESTIN_SZ2089     17.0015397  0.0088051  1930.86   <2e-16 ***
DESTIN_SZ2090     19.1760482  0.0027444  6987.30   <2e-16 ***
DESTIN_SZ2091     14.0647667  0.0665418   211.37   <2e-16 ***
DESTIN_SZ2105     15.9401982  0.0636648   250.38   <2e-16 ***
DESTIN_SZ2106     15.5885926  0.0148891  1046.98   <2e-16 ***
DESTIN_SZ2107     18.2606668  0.0037141  4916.53   <2e-16 ***
DESTIN_SZ2108     18.0256039  0.0045837  3932.55   <2e-16 ***
DESTIN_SZ2109     17.0341340  0.0064513  2640.41   <2e-16 ***
DESTIN_SZ2110     16.4783325  0.0115616  1425.26   <2e-16 ***
DESTIN_SZ2111     15.1465446  0.0329430   459.78   <2e-16 ***
DESTIN_SZ2128     17.2202324  0.0082295  2092.51   <2e-16 ***
DESTIN_SZ2129     16.5528201  0.0098828  1674.91   <2e-16 ***
DESTIN_SZ2130     17.3476185  0.0053464  3244.73   <2e-16 ***
DESTIN_SZ2131     17.4105124  0.0069407  2508.48   <2e-16 ***
DESTIN_SZ2132     17.0130022  0.0074096  2296.07   <2e-16 ***
DESTIN_SZ2148     16.3085207  0.0146352  1114.34   <2e-16 ***
DESTIN_SZ2149     16.3982869  0.0108065  1517.45   <2e-16 ***
DESTIN_SZ2150     16.7223793  0.0081235  2058.51   <2e-16 ***
DESTIN_SZ2151     18.6217838  0.0031665  5880.87   <2e-16 ***
DESTIN_SZ2152     17.7368329  0.0050850  3488.08   <2e-16 ***
DESTIN_SZ2153     16.4151939  0.0111532  1471.79   <2e-16 ***
DESTIN_SZ2171     17.5000225  0.0054451  3213.91   <2e-16 ***
DESTIN_SZ2172     16.3172933  0.0109332  1492.45   <2e-16 ***
DESTIN_SZ2173     16.7742789  0.0072780  2304.78   <2e-16 ***
DESTIN_SZ2174     17.3302208  0.0065154  2659.90   <2e-16 ***
DESTIN_SZ2191     17.5527703  0.0073207  2397.67   <2e-16 ***
DESTIN_SZ2192     16.3931709  0.0107252  1528.47   <2e-16 ***
DESTIN_SZ2193     17.2515636  0.0063032  2736.94   <2e-16 ***
DESTIN_SZ2194     17.3483342  0.0056916  3048.04   <2e-16 ***
DESTIN_SZ2195     15.8344157  0.0354660   446.47   <2e-16 ***
DESTIN_SZ2212     17.5803345  0.0127446  1379.43   <2e-16 ***
DESTIN_SZ2213     17.3429779  0.0080955  2142.29   <2e-16 ***
DESTIN_SZ2214     18.0067877  0.0069758  2581.32   <2e-16 ***
DESTIN_SZ2215     16.4921760  0.0094232  1750.17   <2e-16 ***
DESTIN_SZ2216     17.5061556  0.0060488  2894.17   <2e-16 ***
DESTIN_SZ2233     18.1631439  0.0096552  1881.17   <2e-16 ***
DESTIN_SZ2234     18.2930066  0.0081262  2251.11   <2e-16 ***
DESTIN_SZ2235     17.2635477  0.0087521  1972.51   <2e-16 ***
DESTIN_SZ2236     16.0178504  0.0136219  1175.89   <2e-16 ***
DESTIN_SZ2237     16.8737028  0.0112997  1493.29   <2e-16 ***
DESTIN_SZ2256     17.3481627  0.0119974  1446.00   <2e-16 ***
DESTIN_SZ2257     14.8625823  0.0261906   567.48   <2e-16 ***
DESTIN_SZ2258     16.8838961  0.0073537  2295.97   <2e-16 ***
DESTIN_SZ2259     17.7783318  0.0102016  1742.70   <2e-16 ***
DESTIN_SZ2277     16.1709752  0.0255881   631.97   <2e-16 ***
DESTIN_SZ2278     16.2155661  0.0157684  1028.36   <2e-16 ***
DESTIN_SZ2279     16.9167526  0.0075457  2241.92   <2e-16 ***
DESTIN_SZ2280     15.3121609  0.0311673   491.29   <2e-16 ***
DESTIN_SZ2297     16.1713813  0.0185179   873.28   <2e-16 ***
DESTIN_SZ2300     15.8616765  0.0205042   773.58   <2e-16 ***
DESTIN_SZ2301     16.6383378  0.0098711  1685.55   <2e-16 ***
DESTIN_SZ2318     18.6841212  0.0057960  3223.60   <2e-16 ***
DESTIN_SZ2319     18.5967829  0.0052309  3555.19   <2e-16 ***
DESTIN_SZ2322     17.1295002  0.0091323  1875.71   <2e-16 ***
DESTIN_SZ2337     17.5512708  0.0152767  1148.89   <2e-16 ***
DESTIN_SZ2341     18.9567095  0.0051747  3663.34   <2e-16 ***
DESTIN_SZ2343     16.1664742  0.0128582  1257.29   <2e-16 ***
DESTIN_SZ2361     17.4875772  0.0092317  1894.30   <2e-16 ***
DESTIN_SZ2364     14.9083138  0.0295342   504.78   <2e-16 ***
DESTIN_SZ2379     16.6530440  0.0241213   690.39   <2e-16 ***
DESTIN_SZ2384     18.1613369  0.0066839  2717.16   <2e-16 ***
DESTIN_SZ2405     18.5765284  0.0048050  3866.10   <2e-16 ***
DESTIN_SZ2406     15.5243322  0.0235366   659.58   <2e-16 ***
DESTIN_SZ2426     17.9192434  0.0109187  1641.14   <2e-16 ***
DESTIN_SZ2427     18.1441130  0.0066972  2709.19   <2e-16 ***
DESTIN_SZ2505     18.1648361  0.0181967   998.25   <2e-16 ***
log(BUSINESS_num)         NA         NA       NA       NA    
log(FB_num)               NA         NA       NA       NA    
log(schools_num)          NA         NA       NA       NA    
log(hdb_num)              NA         NA       NA       NA    
log(entertn_num)          NA         NA       NA       NA    
log(dist)         -1.4618825  0.0002562 -5705.39   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 349181331  on 64962  degrees of freedom
Residual deviance:  45737568  on 64142  degrees of freedom
AIC: 46097578

Number of Fisher Scoring iterations: 8

9.4.4 Doubly constrained

Doubly constrained SIM
Code 
dbcSIM <- glm(formula = MORNING_PEAK ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"), data = inter_zonal_flow, na.action = na.exclude)
R-squared

the calculated R-squared is 0.5871965, indicating that the model accounts for approximately 58.72% of the variability in the observed MORNING_PEAK.

Code 
CalcRSquared(dbcSIM$data$MORNING_PEAK, dbcSIM$fitted.values)
[1] 0.5871965
Coefficients
Code 
dbcSIM$coefficients[1]
(Intercept) 
   14.78251
Code 
dbcSIM$coefficients[1635]
DESTIN_SZ2505 
    0.7094831
Summary
Code 
options(max.print = 10000)
summary(dbcSIM)

Call:
glm(formula = MORNING_PEAK ~ ORIGIN_SZ + DESTIN_SZ + log(dist), 
    family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                Estimate Std. Error   z value Pr(>|z|)    
(Intercept)   14.7825131  0.1376669   107.379  < 2e-16 ***
ORIGIN_SZ44    1.8651637  0.1913130     9.749  < 2e-16 ***
ORIGIN_SZ46   -0.4638760  0.1580502    -2.935 0.003336 ** 
ORIGIN_SZ66    0.8207510  0.1832131     4.480 7.47e-06 ***
ORIGIN_SZ67    1.7280743  0.1304829    13.244  < 2e-16 ***
ORIGIN_SZ68   -0.5924438  0.1696234    -3.493 0.000478 ***
ORIGIN_SZ86   -0.4088340  0.1503510    -2.719 0.006544 ** 
ORIGIN_SZ87    3.5035738  0.1480694    23.662  < 2e-16 ***
ORIGIN_SZ88    2.5215503  0.1292031    19.516  < 2e-16 ***
ORIGIN_SZ89    0.2300891  0.1375846     1.672 0.094456 .  
ORIGIN_SZ90    1.0781361  0.1779172     6.060 1.36e-09 ***
ORIGIN_SZ109   0.6458122  0.1567823     4.119 3.80e-05 ***
ORIGIN_SZ110   0.6774575  0.1494445     4.533 5.81e-06 ***
ORIGIN_SZ111   4.0448044  0.1288315    31.396  < 2e-16 ***
ORIGIN_SZ112   0.1521353  0.1453988     1.046 0.295408    
ORIGIN_SZ128   3.3585869  0.1312681    25.586  < 2e-16 ***
ORIGIN_SZ129   0.4780069  0.2187567     2.185 0.028881 *  
ORIGIN_SZ130   1.4046878  0.1390554    10.102  < 2e-16 ***
ORIGIN_SZ131   1.1414313  0.1322103     8.633  < 2e-16 ***
ORIGIN_SZ132   0.2245551  0.1388237     1.618 0.105758    
ORIGIN_SZ133   1.1920048  0.1344194     8.868  < 2e-16 ***
ORIGIN_SZ134   4.3098259  0.1312397    32.839  < 2e-16 ***
ORIGIN_SZ150   4.3536568  0.1297949    33.543  < 2e-16 ***
ORIGIN_SZ151   0.7972520  0.1445269     5.516 3.46e-08 ***
ORIGIN_SZ152   0.2520616  0.1527246     1.650 0.098855 .  
ORIGIN_SZ153   1.6168138  0.1350720    11.970  < 2e-16 ***
ORIGIN_SZ154   4.2669539  0.1283580    33.243  < 2e-16 ***
ORIGIN_SZ155   1.2036839  0.1329298     9.055  < 2e-16 ***
ORIGIN_SZ156   2.1952570  0.1355002    16.201  < 2e-16 ***
ORIGIN_SZ172   2.4447822  0.1435353    17.033  < 2e-16 ***
ORIGIN_SZ174   1.1354702  0.1367109     8.306  < 2e-16 ***
ORIGIN_SZ175   3.8895209  0.1286409    30.235  < 2e-16 ***
ORIGIN_SZ176   4.9927160  0.1282428    38.932  < 2e-16 ***
ORIGIN_SZ195   0.1461498  0.1503134     0.972 0.330901    
ORIGIN_SZ196   1.1205023  0.1339388     8.366  < 2e-16 ***
ORIGIN_SZ197   0.2039552  0.1785044     1.143 0.253214    
ORIGIN_SZ215   1.7228934  0.1548747    11.124  < 2e-16 ***
ORIGIN_SZ216   5.3512021  0.1283651    41.687  < 2e-16 ***
ORIGIN_SZ217   2.4696949  0.1299800    19.001  < 2e-16 ***
ORIGIN_SZ237  -0.1148070  0.2104278    -0.546 0.585349    
ORIGIN_SZ238   0.9871565  0.1467267     6.728 1.72e-11 ***
ORIGIN_SZ239   1.2506722  0.1870828     6.685 2.31e-11 ***
ORIGIN_SZ257   0.2715459  0.1408892     1.927 0.053933 .  
ORIGIN_SZ258   2.2349763  0.1314398    17.004  < 2e-16 ***
ORIGIN_SZ259   1.6038725  0.1342585    11.946  < 2e-16 ***
ORIGIN_SZ278   1.8380732  0.1332248    13.797  < 2e-16 ***
ORIGIN_SZ279   0.6102791  0.1357349     4.496 6.92e-06 ***
ORIGIN_SZ280   1.0967209  0.1369188     8.010 1.15e-15 ***
ORIGIN_SZ298  -2.9525019  0.3573065    -8.263  < 2e-16 ***
ORIGIN_SZ299   0.4052485  0.1386668     2.922 0.003473 ** 
ORIGIN_SZ300   4.2242256  0.1285551    32.859  < 2e-16 ***
ORIGIN_SZ320  -0.1304437  0.1374289    -0.949 0.342533    
ORIGIN_SZ321   1.0223496  0.1486339     6.878 6.06e-12 ***
ORIGIN_SZ322   2.1303020  0.1344205    15.848  < 2e-16 ***
ORIGIN_SZ340   1.7776512  0.1312870    13.540  < 2e-16 ***
ORIGIN_SZ341   0.1698864  0.1359914     1.249 0.211576    
ORIGIN_SZ342   2.0446107  0.1344315    15.209  < 2e-16 ***
ORIGIN_SZ363   1.7399036  0.1336962    13.014  < 2e-16 ***
ORIGIN_SZ364   2.2324348  0.1310346    17.037  < 2e-16 ***
ORIGIN_SZ383   1.2662322  0.1319317     9.598  < 2e-16 ***
ORIGIN_SZ384   0.4729125  0.1372673     3.445 0.000571 ***
ORIGIN_SZ385   1.6732365  0.1364878    12.259  < 2e-16 ***
ORIGIN_SZ404   2.2671817  0.1316880    17.216  < 2e-16 ***
ORIGIN_SZ405   0.6452881  0.1382800     4.667 3.06e-06 ***
ORIGIN_SZ406   6.0984179  0.1282803    47.540  < 2e-16 ***
ORIGIN_SZ407   2.3074859  0.1341287    17.204  < 2e-16 ***
ORIGIN_SZ408   3.0326485  0.1298347    23.358  < 2e-16 ***
ORIGIN_SZ425  -0.4946901  0.1608092    -3.076 0.002096 ** 
ORIGIN_SZ426   1.5311039  0.1318184    11.615  < 2e-16 ***
ORIGIN_SZ427   0.9190448  0.1350628     6.805 1.01e-11 ***
ORIGIN_SZ428   1.0913201  0.1480848     7.370 1.71e-13 ***
ORIGIN_SZ429   2.5227525  0.1294959    19.481  < 2e-16 ***
ORIGIN_SZ446   1.4303619  0.1412628    10.126  < 2e-16 ***
ORIGIN_SZ447   0.7386870  0.1344585     5.494 3.93e-08 ***
ORIGIN_SZ448   1.9352844  0.1310960    14.762  < 2e-16 ***
ORIGIN_SZ449   5.2559562  0.1284385    40.922  < 2e-16 ***
ORIGIN_SZ450   2.2474602  0.1294904    17.356  < 2e-16 ***
ORIGIN_SZ468   1.9333540  0.1318865    14.659  < 2e-16 ***
ORIGIN_SZ469   3.1703947  0.1291647    24.545  < 2e-16 ***
ORIGIN_SZ470   5.2270506  0.1283788    40.716  < 2e-16 ***
ORIGIN_SZ471   3.2081727  0.1291587    24.839  < 2e-16 ***
ORIGIN_SZ488   0.8657735  0.1398141     6.192 5.93e-10 ***
ORIGIN_SZ489  -0.8857821  0.2053213    -4.314 1.60e-05 ***
ORIGIN_SZ490   3.6851496  0.1288719    28.595  < 2e-16 ***
ORIGIN_SZ491   4.1880606  0.1285170    32.588  < 2e-16 ***
ORIGIN_SZ493  -1.1749485  0.2122468    -5.536 3.10e-08 ***
ORIGIN_SZ494   1.2353383  0.1428587     8.647  < 2e-16 ***
ORIGIN_SZ509   0.7461932  0.1334786     5.590 2.27e-08 ***
ORIGIN_SZ510   1.5711689  0.1308049    12.012  < 2e-16 ***
ORIGIN_SZ511   3.1384338  0.1287544    24.375  < 2e-16 ***
ORIGIN_SZ512   5.8131536  0.1283280    45.299  < 2e-16 ***
ORIGIN_SZ513   2.3201534  0.1306174    17.763  < 2e-16 ***
ORIGIN_SZ514   2.1168213  0.1340983    15.786  < 2e-16 ***
ORIGIN_SZ515   0.3959269  0.1995066     1.985 0.047197 *  
ORIGIN_SZ530  -0.1051997  0.1551347    -0.678 0.497697    
ORIGIN_SZ531   2.1354352  0.1298169    16.450  < 2e-16 ***
ORIGIN_SZ532   1.5154353  0.1307571    11.590  < 2e-16 ***
ORIGIN_SZ533   5.5870356  0.1283265    43.538  < 2e-16 ***
ORIGIN_SZ534   6.1313157  0.1283403    47.774  < 2e-16 ***
ORIGIN_SZ536   2.8040298  0.1308424    21.431  < 2e-16 ***
ORIGIN_SZ537   0.9009629  0.1773825     5.079 3.79e-07 ***
ORIGIN_SZ538   0.7319978  0.2448586     2.989 0.002795 ** 
ORIGIN_SZ539   0.1889885  1.0087880     0.187 0.851392    
ORIGIN_SZ551  -0.0802166  0.1389218    -0.577 0.563654    
ORIGIN_SZ552   2.3580939  0.1334290    17.673  < 2e-16 ***
ORIGIN_SZ553   1.9548006  0.1294728    15.098  < 2e-16 ***
ORIGIN_SZ554   5.4436879  0.1283357    42.418  < 2e-16 ***
ORIGIN_SZ555   4.7990556  0.1284894    37.350  < 2e-16 ***
ORIGIN_SZ559   1.3434072  0.1615223     8.317  < 2e-16 ***
ORIGIN_SZ560   3.7651027  0.1360404    27.676  < 2e-16 ***
ORIGIN_SZ561  -1.3562021  1.0094990    -1.343 0.179129    
ORIGIN_SZ572  -1.8802721  0.4282239    -4.391 1.13e-05 ***
ORIGIN_SZ573   0.4595648  0.1350553     3.403 0.000667 ***
ORIGIN_SZ574   1.8237630  0.1334734    13.664  < 2e-16 ***
ORIGIN_SZ575   6.5891046  0.1283083    51.354  < 2e-16 ***
ORIGIN_SZ576   5.0716420  0.1283839    39.504  < 2e-16 ***
ORIGIN_SZ578   0.3477660  0.1612539     2.157 0.031034 *  
ORIGIN_SZ582   0.7041518  0.1661964     4.237 2.27e-05 ***
ORIGIN_SZ583   0.6990335  0.4279531     1.633 0.102378    
ORIGIN_SZ584   4.2195182  0.1384317    30.481  < 2e-16 ***
ORIGIN_SZ593   1.5726840  0.1370901    11.472  < 2e-16 ***
ORIGIN_SZ594   1.5817148  0.1308139    12.091  < 2e-16 ***
ORIGIN_SZ595   1.8243274  0.1296637    14.070  < 2e-16 ***
ORIGIN_SZ596   4.8396880  0.1283597    37.704  < 2e-16 ***
ORIGIN_SZ597   2.0869369  0.1405580    14.848  < 2e-16 ***
ORIGIN_SZ603   1.3234042  0.1692391     7.820 5.29e-15 ***
ORIGIN_SZ604   1.7550673  0.2231652     7.864 3.71e-15 ***
ORIGIN_SZ615   0.2206062  0.1363140     1.618 0.105583    
ORIGIN_SZ616   1.2829325  0.1320936     9.712  < 2e-16 ***
ORIGIN_SZ617   2.1648199  0.1295708    16.708  < 2e-16 ***
ORIGIN_SZ618   5.5155910  0.1283468    42.974  < 2e-16 ***
ORIGIN_SZ620   2.6761751  0.1317617    20.311  < 2e-16 ***
ORIGIN_SZ637   1.0365392  0.1348394     7.687 1.50e-14 ***
ORIGIN_SZ638   4.9647838  0.1283593    38.679  < 2e-16 ***
ORIGIN_SZ657   2.8464046  0.1293749    22.001  < 2e-16 ***
ORIGIN_SZ658   4.3118367  0.1284518    33.568  < 2e-16 ***
ORIGIN_SZ659   4.5165384  0.1284061    35.174  < 2e-16 ***
ORIGIN_SZ660   5.6795444  0.1283370    44.255  < 2e-16 ***
ORIGIN_SZ662   5.6490277  0.1285159    43.956  < 2e-16 ***
ORIGIN_SZ677   2.7261064  0.1302955    20.922  < 2e-16 ***
ORIGIN_SZ678   0.5485599  0.1364948     4.019 5.85e-05 ***
ORIGIN_SZ679   5.5476455  0.1283465    43.224  < 2e-16 ***
ORIGIN_SZ680   5.7814553  0.1283449    45.046  < 2e-16 ***
ORIGIN_SZ681   4.4894509  0.1285630    34.920  < 2e-16 ***
ORIGIN_SZ699   2.2405240  0.1302647    17.200  < 2e-16 ***
ORIGIN_SZ700   4.4925825  0.1284369    34.979  < 2e-16 ***
ORIGIN_SZ701   4.4095803  0.1284380    34.332  < 2e-16 ***
ORIGIN_SZ702   5.4786781  0.1283432    42.688  < 2e-16 ***
ORIGIN_SZ704   2.5640128  0.1322083    19.394  < 2e-16 ***
ORIGIN_SZ722   2.2596147  0.1295939    17.436  < 2e-16 ***
ORIGIN_SZ725   2.0324175  0.1345148    15.109  < 2e-16 ***
ORIGIN_SZ741   2.7762245  0.1293588    21.461  < 2e-16 ***
ORIGIN_SZ743   2.9902364  0.1288881    23.200  < 2e-16 ***
ORIGIN_SZ744   5.0780767  0.1283722    39.557  < 2e-16 ***
ORIGIN_SZ761   2.3192045  0.1312756    17.667  < 2e-16 ***
ORIGIN_SZ762   4.2846462  0.1285059    33.342  < 2e-16 ***
ORIGIN_SZ763   1.5206569  0.1310794    11.601  < 2e-16 ***
ORIGIN_SZ764   5.5790146  0.1283416    43.470  < 2e-16 ***
ORIGIN_SZ765   4.7777270  0.1285630    37.163  < 2e-16 ***
ORIGIN_SZ767   6.6070303  0.1283571    51.474  < 2e-16 ***
ORIGIN_SZ772   1.3281976  0.1484396     8.948  < 2e-16 ***
ORIGIN_SZ784   1.3670047  0.1310123    10.434  < 2e-16 ***
ORIGIN_SZ785   4.6756446  0.1283700    36.423  < 2e-16 ***
ORIGIN_SZ786   4.3556867  0.1284389    33.913  < 2e-16 ***
ORIGIN_SZ787   4.9407778  0.1285040    38.448  < 2e-16 ***
ORIGIN_SZ788   5.7989893  0.1284141    45.159  < 2e-16 ***
ORIGIN_SZ789   4.2570120  0.1287218    33.071  < 2e-16 ***
ORIGIN_SZ803   0.5015402  0.1388696     3.612 0.000304 ***
ORIGIN_SZ804   5.3266445  0.1283676    41.495  < 2e-16 ***
ORIGIN_SZ805   5.2948963  0.1283446    41.255  < 2e-16 ***
ORIGIN_SZ806   5.0165155  0.1283678    39.079  < 2e-16 ***
ORIGIN_SZ807   6.0112348  0.1283728    46.826  < 2e-16 ***
ORIGIN_SZ808   4.2397833  0.1287592    32.928  < 2e-16 ***
ORIGIN_SZ809   6.0018355  0.1283491    46.762  < 2e-16 ***
ORIGIN_SZ810   5.2248926  0.1284356    40.681  < 2e-16 ***
ORIGIN_SZ814   3.1415033  0.1311682    23.950  < 2e-16 ***
ORIGIN_SZ819   5.2782677  0.1295641    40.739  < 2e-16 ***
ORIGIN_SZ824   1.4838427  0.1338729    11.084  < 2e-16 ***
ORIGIN_SZ826   2.9697079  0.1286813    23.078  < 2e-16 ***
ORIGIN_SZ827   4.9601290  0.1283584    38.643  < 2e-16 ***
ORIGIN_SZ828   5.3539759  0.1283522    41.713  < 2e-16 ***
ORIGIN_SZ829   5.4057517  0.1283801    42.107  < 2e-16 ***
ORIGIN_SZ830   5.6207518  0.1284042    43.774  < 2e-16 ***
ORIGIN_SZ831   6.5320399  0.1283357    50.898  < 2e-16 ***
ORIGIN_SZ832   5.6900053  0.1284630    44.293  < 2e-16 ***
ORIGIN_SZ835   3.0146096  0.1315282    22.920  < 2e-16 ***
ORIGIN_SZ844   0.4681830  0.1482345     3.158 0.001586 ** 
ORIGIN_SZ846   4.3998432  0.1284074    34.265  < 2e-16 ***
ORIGIN_SZ847   3.5040945  0.1286150    27.245  < 2e-16 ***
ORIGIN_SZ848   4.7250679  0.1283870    36.803  < 2e-16 ***
ORIGIN_SZ849   3.9550633  0.1285238    30.773  < 2e-16 ***
ORIGIN_SZ850   4.8690494  0.1284142    37.917  < 2e-16 ***
ORIGIN_SZ851   5.4253340  0.1283676    42.264  < 2e-16 ***
ORIGIN_SZ852   4.9548384  0.1284522    38.573  < 2e-16 ***
ORIGIN_SZ853   6.9365719  0.1283778    54.032  < 2e-16 ***
ORIGIN_SZ854   3.2237110  0.1308010    24.646  < 2e-16 ***
ORIGIN_SZ855   1.8416130  0.1353800    13.603  < 2e-16 ***
ORIGIN_SZ856   3.4683981  0.1296780    26.746  < 2e-16 ***
ORIGIN_SZ866   2.3172711  0.1310822    17.678  < 2e-16 ***
ORIGIN_SZ867   3.1976249  0.1288244    24.822  < 2e-16 ***
ORIGIN_SZ868   2.4882976  0.1294932    19.216  < 2e-16 ***
ORIGIN_SZ869   5.0233449  0.1284450    39.109  < 2e-16 ***
ORIGIN_SZ870   5.9104196  0.1283334    46.055  < 2e-16 ***
ORIGIN_SZ871   5.7459917  0.1284312    44.740  < 2e-16 ***
ORIGIN_SZ872   3.6190123  0.1287687    28.105  < 2e-16 ***
ORIGIN_SZ873   3.8506553  0.1286792    29.924  < 2e-16 ***
ORIGIN_SZ874   4.1234873  0.1285464    32.078  < 2e-16 ***
ORIGIN_SZ875   1.0949378  0.1438786     7.610 2.74e-14 ***
ORIGIN_SZ876   2.2269604  0.1318447    16.891  < 2e-16 ***
ORIGIN_SZ877   1.7867469  0.1341387    13.320  < 2e-16 ***
ORIGIN_SZ887   2.6306026  0.1289823    20.395  < 2e-16 ***
ORIGIN_SZ888   4.1253397  0.1284797    32.109  < 2e-16 ***
ORIGIN_SZ889   1.0535960  0.1320251     7.980 1.46e-15 ***
ORIGIN_SZ890   5.3284587  0.1283518    41.514  < 2e-16 ***
ORIGIN_SZ891   4.0268547  0.1287780    31.270  < 2e-16 ***
ORIGIN_SZ893   5.4681295  0.1283613    42.600  < 2e-16 ***
ORIGIN_SZ894   3.6741126  0.1287171    28.544  < 2e-16 ***
ORIGIN_SZ895   3.1918333  0.1291808    24.708  < 2e-16 ***
ORIGIN_SZ896   1.9784262  0.1315361    15.041  < 2e-16 ***
ORIGIN_SZ897   0.3264987  0.1420392     2.299 0.021525 *  
ORIGIN_SZ898   2.5017205  0.1320423    18.946  < 2e-16 ***
ORIGIN_SZ908   4.1028770  0.1288535    31.841  < 2e-16 ***
ORIGIN_SZ909   4.1157508  0.1284197    32.049  < 2e-16 ***
ORIGIN_SZ910   2.1546228  0.1293238    16.661  < 2e-16 ***
ORIGIN_SZ911   3.5439302  0.1285925    27.559  < 2e-16 ***
ORIGIN_SZ912   5.0794681  0.1283673    39.570  < 2e-16 ***
ORIGIN_SZ915   5.3722279  0.1283714    41.849  < 2e-16 ***
ORIGIN_SZ917   4.8669273  0.1285088    37.872  < 2e-16 ***
ORIGIN_SZ918   1.1976582  0.1338619     8.947  < 2e-16 ***
ORIGIN_SZ919   4.1125271  0.1286438    31.968  < 2e-16 ***
ORIGIN_SZ928   3.0455756  0.1289702    23.615  < 2e-16 ***
ORIGIN_SZ929   4.4978222  0.1283770    35.036  < 2e-16 ***
ORIGIN_SZ930   5.3657820  0.1283355    41.811  < 2e-16 ***
ORIGIN_SZ931   2.3162035  0.1293690    17.904  < 2e-16 ***
ORIGIN_SZ932   2.7694625  0.1294770    21.390  < 2e-16 ***
ORIGIN_SZ933   4.9357933  0.1284184    38.435  < 2e-16 ***
ORIGIN_SZ934   2.3306921  0.1296816    17.972  < 2e-16 ***
ORIGIN_SZ935   6.2496853  0.1283348    48.698  < 2e-16 ***
ORIGIN_SZ938  -1.6147369  0.2810424    -5.746 9.16e-09 ***
ORIGIN_SZ939   6.2324982  0.1283674    48.552  < 2e-16 ***
ORIGIN_SZ940   0.4374257  0.1465384     2.985 0.002835 ** 
ORIGIN_SZ949   2.7913292  0.1289455    21.647  < 2e-16 ***
ORIGIN_SZ950   4.9625752  0.1283901    38.652  < 2e-16 ***
ORIGIN_SZ951   5.8124044  0.1283280    45.293  < 2e-16 ***
ORIGIN_SZ952   2.5331222  0.1298464    19.509  < 2e-16 ***
ORIGIN_SZ953   3.7049359  0.1286368    28.802  < 2e-16 ***
ORIGIN_SZ954   2.5590881  0.1293518    19.784  < 2e-16 ***
ORIGIN_SZ955   4.8206888  0.1284189    37.539  < 2e-16 ***
ORIGIN_SZ956   3.2253869  0.1287870    25.044  < 2e-16 ***
ORIGIN_SZ957   5.3750668  0.1284242    41.854  < 2e-16 ***
ORIGIN_SZ959   1.4277296  0.1368777    10.431  < 2e-16 ***
ORIGIN_SZ961   1.4545836  0.1317928    11.037  < 2e-16 ***
ORIGIN_SZ962   6.7795777  0.1284728    52.771  < 2e-16 ***
ORIGIN_SZ970   3.3200875  0.1285368    25.830  < 2e-16 ***
ORIGIN_SZ971   4.6872948  0.1283546    36.518  < 2e-16 ***
ORIGIN_SZ972   4.5754058  0.1283801    35.640  < 2e-16 ***
ORIGIN_SZ974   4.2151790  0.1284972    32.804  < 2e-16 ***
ORIGIN_SZ975   3.8529613  0.1285929    29.962  < 2e-16 ***
ORIGIN_SZ976   2.5736286  0.1293162    19.902  < 2e-16 ***
ORIGIN_SZ977   5.7393499  0.1283528    44.715  < 2e-16 ***
ORIGIN_SZ978   5.6271784  0.1284820    43.797  < 2e-16 ***
ORIGIN_SZ982   2.5287621  0.1291557    19.579  < 2e-16 ***
ORIGIN_SZ983   7.4453499  0.1283646    58.002  < 2e-16 ***
ORIGIN_SZ984   7.4937210  0.1283984    58.363  < 2e-16 ***
ORIGIN_SZ991   3.3688268  0.1285932    26.198  < 2e-16 ***
ORIGIN_SZ992   3.6566784  0.1284744    28.462  < 2e-16 ***
ORIGIN_SZ993   3.4070732  0.1285045    26.513  < 2e-16 ***
ORIGIN_SZ994   2.9499187  0.1287275    22.916  < 2e-16 ***
ORIGIN_SZ995   4.3993511  0.1284162    34.259  < 2e-16 ***
ORIGIN_SZ996   4.1139306  0.1285169    32.011  < 2e-16 ***
ORIGIN_SZ997   2.8308973  0.1311854    21.579  < 2e-16 ***
ORIGIN_SZ998   5.8555628  0.1283574    45.619  < 2e-16 ***
ORIGIN_SZ999   5.8385828  0.1284204    45.465  < 2e-16 ***
ORIGIN_SZ1001  2.6713211  0.1306592    20.445  < 2e-16 ***
ORIGIN_SZ1003  5.3580592  0.1283740    41.738  < 2e-16 ***
ORIGIN_SZ1004  6.0074265  0.1283503    46.805  < 2e-16 ***
ORIGIN_SZ1011  1.3614625  0.1319247    10.320  < 2e-16 ***
ORIGIN_SZ1012  1.3964150  0.1321703    10.565  < 2e-16 ***
ORIGIN_SZ1013  2.1051864  0.1293209    16.279  < 2e-16 ***
ORIGIN_SZ1014  2.9620901  0.1287294    23.010  < 2e-16 ***
ORIGIN_SZ1015  2.4138370  0.1291886    18.685  < 2e-16 ***
ORIGIN_SZ1016  4.1555792  0.1284861    32.343  < 2e-16 ***
ORIGIN_SZ1018  4.7337897  0.1286573    36.794  < 2e-16 ***
ORIGIN_SZ1019  6.3123786  0.1283874    49.167  < 2e-16 ***
ORIGIN_SZ1023  4.3697894  0.1286306    33.972  < 2e-16 ***
ORIGIN_SZ1024  5.3946861  0.1283850    42.020  < 2e-16 ***
ORIGIN_SZ1025  0.5797077  0.1378446     4.206 2.60e-05 ***
ORIGIN_SZ1033  2.7628241  0.1287715    21.455  < 2e-16 ***
ORIGIN_SZ1034  3.7076914  0.1284935    28.855  < 2e-16 ***
ORIGIN_SZ1035  4.4197167  0.1284092    34.419  < 2e-16 ***
ORIGIN_SZ1036  2.4413074  0.1291227    18.907  < 2e-16 ***
ORIGIN_SZ1037  3.6810703  0.1284912    28.648  < 2e-16 ***
ORIGIN_SZ1043  2.7041178  0.1306722    20.694  < 2e-16 ***
ORIGIN_SZ1045  5.0036359  0.1283827    38.974  < 2e-16 ***
ORIGIN_SZ1046  4.8600249  0.1284019    37.850  < 2e-16 ***
ORIGIN_SZ1053  4.2805812  0.1284235    33.332  < 2e-16 ***
ORIGIN_SZ1054  3.1721677  0.1285584    24.675  < 2e-16 ***
ORIGIN_SZ1055  4.3164605  0.1284015    33.617  < 2e-16 ***
ORIGIN_SZ1056  3.3449664  0.1286159    26.007  < 2e-16 ***
ORIGIN_SZ1064  0.3641541  0.2684429     1.357 0.174927    
ORIGIN_SZ1066  4.7807553  0.1284028    37.232  < 2e-16 ***
ORIGIN_SZ1067  5.5362003  0.1284055    43.115  < 2e-16 ***
ORIGIN_SZ1074  3.6129635  0.1285148    28.113  < 2e-16 ***
ORIGIN_SZ1075  2.8313889  0.1287176    21.997  < 2e-16 ***
ORIGIN_SZ1076  3.0018657  0.1285817    23.346  < 2e-16 ***
ORIGIN_SZ1077  3.2299883  0.1286726    25.102  < 2e-16 ***
ORIGIN_SZ1079  4.6158888  0.1284070    35.947  < 2e-16 ***
ORIGIN_SZ1085 -1.6741102  0.2142978    -7.812 5.63e-15 ***
ORIGIN_SZ1087  4.5588996  0.1284355    35.496  < 2e-16 ***
ORIGIN_SZ1088  3.0334034  0.1288400    23.544  < 2e-16 ***
ORIGIN_SZ1094  1.6330476  0.1355237    12.050  < 2e-16 ***
ORIGIN_SZ1095  1.0000862  0.1337777     7.476 7.68e-14 ***
ORIGIN_SZ1096  2.9821904  0.1298896    22.959  < 2e-16 ***
ORIGIN_SZ1097  5.0906615  0.1283501    39.662  < 2e-16 ***
ORIGIN_SZ1098  2.6108029  0.1295066    20.160  < 2e-16 ***
ORIGIN_SZ1099  4.0158899  0.1284725    31.259  < 2e-16 ***
ORIGIN_SZ1105  1.7724246  0.1429485    12.399  < 2e-16 ***
ORIGIN_SZ1106  0.0153603  0.1613298     0.095 0.924147    
ORIGIN_SZ1107  2.3455815  0.1314244    17.847  < 2e-16 ***
ORIGIN_SZ1108  6.6047138  0.1283347    51.465  < 2e-16 ***
ORIGIN_SZ1109  3.9159747  0.1285455    30.464  < 2e-16 ***
ORIGIN_SZ1116  3.3236220  0.1285814    25.848  < 2e-16 ***
ORIGIN_SZ1117  1.7078013  0.1298638    13.151  < 2e-16 ***
ORIGIN_SZ1118  2.2710221  0.1295121    17.535  < 2e-16 ***
ORIGIN_SZ1119  3.2002136  0.1286806    24.869  < 2e-16 ***
ORIGIN_SZ1120  3.1584771  0.1289782    24.488  < 2e-16 ***
ORIGIN_SZ1129  5.0437158  0.1283974    39.282  < 2e-16 ***
ORIGIN_SZ1130  5.0856121  0.1283706    39.617  < 2e-16 ***
ORIGIN_SZ1131  4.4503068  0.1285519    34.619  < 2e-16 ***
ORIGIN_SZ1136  2.3574337  0.1290568    18.267  < 2e-16 ***
ORIGIN_SZ1138  0.9244841  0.1329645     6.953 3.58e-12 ***
ORIGIN_SZ1139  4.1524155  0.1284025    32.339  < 2e-16 ***
ORIGIN_SZ1141  4.1071977  0.1284565    31.973  < 2e-16 ***
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ORIGIN_SZ1150  5.3044536  0.1283620    41.324  < 2e-16 ***
ORIGIN_SZ1151  4.2082018  0.1284711    32.756  < 2e-16 ***
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ORIGIN_SZ1159  3.9526476  0.1284212    30.779  < 2e-16 ***
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ORIGIN_SZ1194  2.8688838  0.1290323    22.234  < 2e-16 ***
ORIGIN_SZ1200  3.4689356  0.1284773    27.000  < 2e-16 ***
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ORIGIN_SZ1242  3.3558722  0.1284773    26.120  < 2e-16 ***
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ORIGIN_SZ1278  2.7968417  0.1289899    21.683  < 2e-16 ***
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ORIGIN_SZ1285  4.8056051  0.1283510    37.441  < 2e-16 ***
ORIGIN_SZ1286  3.0869296  0.1286914    23.987  < 2e-16 ***
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ORIGIN_SZ1295  2.6145693  0.1299450    20.121  < 2e-16 ***
ORIGIN_SZ1298  4.3456426  0.1284881    33.821  < 2e-16 ***
ORIGIN_SZ1299  4.5959685  0.1284570    35.778  < 2e-16 ***
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ORIGIN_SZ1305  4.1335815  0.1283719    32.200  < 2e-16 ***
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ORIGIN_SZ1308  3.9720413  0.1284550    30.922  < 2e-16 ***
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ORIGIN_SZ1317  3.3278269  0.1288029    25.837  < 2e-16 ***
ORIGIN_SZ1318  2.6193558  0.1292355    20.268  < 2e-16 ***
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ORIGIN_SZ1320  4.0232570  0.1286368    31.276  < 2e-16 ***
ORIGIN_SZ1325  2.3380308  0.1288702    18.143  < 2e-16 ***
ORIGIN_SZ1326  4.3044463  0.1283701    33.532  < 2e-16 ***
ORIGIN_SZ1327  4.1268654  0.1283838    32.145  < 2e-16 ***
ORIGIN_SZ1328  2.7620098  0.1286476    21.470  < 2e-16 ***
ORIGIN_SZ1329  3.0506402  0.1288063    23.684  < 2e-16 ***
ORIGIN_SZ1330  3.8621532  0.1285638    30.041  < 2e-16 ***
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ORIGIN_SZ1334  3.5087803  0.1287888    27.244  < 2e-16 ***
ORIGIN_SZ1335  3.0465284  0.1293834    23.547  < 2e-16 ***
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ORIGIN_SZ1347  4.9832894  0.1283510    38.825  < 2e-16 ***
ORIGIN_SZ1348  3.3585153  0.1284571    26.145  < 2e-16 ***
ORIGIN_SZ1349  3.1967346  0.1285549    24.867  < 2e-16 ***
ORIGIN_SZ1350  3.4336485  0.1287568    26.668  < 2e-16 ***
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ORIGIN_SZ1354  2.9970965  0.1289125    23.249  < 2e-16 ***
ORIGIN_SZ1355  3.8129551  0.1285760    29.655  < 2e-16 ***
ORIGIN_SZ1357  2.8838085  0.1296157    22.249  < 2e-16 ***
ORIGIN_SZ1358  4.2012475  0.1285152    32.691  < 2e-16 ***
ORIGIN_SZ1359  4.5175512  0.1284159    35.179  < 2e-16 ***
ORIGIN_SZ1360  4.5560472  0.1284234    35.477  < 2e-16 ***
ORIGIN_SZ1361  5.7082420  0.1283801    44.464  < 2e-16 ***
ORIGIN_SZ1362  1.8192252  0.1342208    13.554  < 2e-16 ***
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ORIGIN_SZ1370  3.8036915  0.1284010    29.624  < 2e-16 ***
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ORIGIN_SZ1375  4.2928205  0.1285257    33.400  < 2e-16 ***
ORIGIN_SZ1376  3.5917491  0.1289104    27.862  < 2e-16 ***
ORIGIN_SZ1379  1.7826380  0.1328203    13.421  < 2e-16 ***
ORIGIN_SZ1380  5.9283182  0.1283474    46.190  < 2e-16 ***
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ORIGIN_SZ1383  2.5047943  0.1306096    19.178  < 2e-16 ***
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ORIGIN_SZ1390  3.3067639  0.1284756    25.738  < 2e-16 ***
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ORIGIN_SZ1393  2.0483419  0.1291043    15.866  < 2e-16 ***
ORIGIN_SZ1394  3.8051463  0.1284633    29.620  < 2e-16 ***
ORIGIN_SZ1395  3.5510811  0.1285136    27.632  < 2e-16 ***
ORIGIN_SZ1396  4.6180112  0.1284032    35.965  < 2e-16 ***
ORIGIN_SZ1397  4.6804762  0.1284120    36.449  < 2e-16 ***
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ORIGIN_SZ1400  4.6759075  0.1284756    36.395  < 2e-16 ***
ORIGIN_SZ1401  5.0477274  0.1283715    39.321  < 2e-16 ***
ORIGIN_SZ1402  5.1011623  0.1283864    39.733  < 2e-16 ***
ORIGIN_SZ1404  5.1579558  0.1291829    39.928  < 2e-16 ***
ORIGIN_SZ1410  4.0420432  0.1283783    31.485  < 2e-16 ***
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ORIGIN_SZ1413  4.0506420  0.1284059    31.546  < 2e-16 ***
ORIGIN_SZ1414  3.4833687  0.1284556    27.117  < 2e-16 ***
ORIGIN_SZ1415  2.9922201  0.1286207    23.264  < 2e-16 ***
ORIGIN_SZ1416  3.6221805  0.1284861    28.191  < 2e-16 ***
ORIGIN_SZ1417  3.7745313  0.1284677    29.381  < 2e-16 ***
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ORIGIN_SZ1422  5.1072716  0.1284094    39.773  < 2e-16 ***
ORIGIN_SZ1423  6.0174788  0.1283608    46.879  < 2e-16 ***
ORIGIN_SZ1430  3.7176173  0.1284346    28.946  < 2e-16 ***
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ORIGIN_SZ1432  3.8109774  0.1283933    29.682  < 2e-16 ***
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ORIGIN_SZ1434  4.0586775  0.1284137    31.606  < 2e-16 ***
ORIGIN_SZ1435  4.4171474  0.1283683    34.410  < 2e-16 ***
ORIGIN_SZ1436  1.3014336  0.1303414     9.985  < 2e-16 ***
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ORIGIN_SZ1438  5.0522959  0.1283502    39.363  < 2e-16 ***
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ORIGIN_SZ1444  5.0405899  0.1285228    39.219  < 2e-16 ***
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ORIGIN_SZ1453  3.0191038  0.1285082    23.493  < 2e-16 ***
ORIGIN_SZ1454  2.0338914  0.1295590    15.699  < 2e-16 ***
ORIGIN_SZ1455  3.3886706  0.1285616    26.358  < 2e-16 ***
ORIGIN_SZ1456  3.8310384  0.1284343    29.829  < 2e-16 ***
ORIGIN_SZ1457  4.6346391  0.1283695    36.104  < 2e-16 ***
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ORIGIN_SZ1459  4.4130417  0.1283861    34.373  < 2e-16 ***
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ORIGIN_SZ1547  1.3944409  0.1408842     9.898  < 2e-16 ***
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ORIGIN_SZ1559  4.1062899  0.1283844    31.984  < 2e-16 ***
ORIGIN_SZ1560  4.9133558  0.1283512    38.281  < 2e-16 ***
ORIGIN_SZ1561  4.7433747  0.1283807    36.948  < 2e-16 ***
ORIGIN_SZ1562  1.7916994  0.1297135    13.813  < 2e-16 ***
ORIGIN_SZ1563  3.6182330  0.1284897    28.160  < 2e-16 ***
ORIGIN_SZ1564  2.7474915  0.1289386    21.309  < 2e-16 ***
ORIGIN_SZ1565  2.8419407  0.1289732    22.035  < 2e-16 ***
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ORIGIN_SZ1581  1.3677498  0.1296889    10.546  < 2e-16 ***
ORIGIN_SZ1582  4.6045623  0.1283575    35.873  < 2e-16 ***
ORIGIN_SZ1583  2.8642254  0.1297258    22.079  < 2e-16 ***
ORIGIN_SZ1584  3.1251714  0.1286746    24.287  < 2e-16 ***
ORIGIN_SZ1585  3.8128714  0.1285971    29.650  < 2e-16 ***
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ORIGIN_SZ1589  1.7206351  0.1334863    12.890  < 2e-16 ***
ORIGIN_SZ1590  1.2315089  0.1435987     8.576  < 2e-16 ***
ORIGIN_SZ1600  4.7154141  0.1286556    36.651  < 2e-16 ***
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ORIGIN_SZ1603  4.8145991  0.1283601    37.509  < 2e-16 ***
ORIGIN_SZ1604  3.2985528  0.1285190    25.666  < 2e-16 ***
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ORIGIN_SZ1607  3.4365748  0.1286286    26.717  < 2e-16 ***
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ORIGIN_SZ1610  1.8098403  0.1416268    12.779  < 2e-16 ***
ORIGIN_SZ1622  3.2746454  0.1298294    25.223  < 2e-16 ***
ORIGIN_SZ1623  4.5686096  0.1283625    35.591  < 2e-16 ***
ORIGIN_SZ1624  3.3451251  0.1285342    26.025  < 2e-16 ***
ORIGIN_SZ1625  4.7448807  0.1283786    36.960  < 2e-16 ***
ORIGIN_SZ1626  5.4031403  0.1283445    42.099  < 2e-16 ***
ORIGIN_SZ1627  3.7636640  0.1284854    29.293  < 2e-16 ***
ORIGIN_SZ1628  5.5191293  0.1283478    43.001  < 2e-16 ***
ORIGIN_SZ1629  4.4870676  0.1284694    34.927  < 2e-16 ***
ORIGIN_SZ1630  4.5796065  0.1285216    35.633  < 2e-16 ***
ORIGIN_SZ1631  1.1315331  0.1389935     8.141 3.92e-16 ***
ORIGIN_SZ1642  2.1664333  0.1309212    16.548  < 2e-16 ***
ORIGIN_SZ1643  4.5066494  0.1283725    35.106  < 2e-16 ***
ORIGIN_SZ1644  2.2746032  0.1292608    17.597  < 2e-16 ***
ORIGIN_SZ1645  3.7832826  0.1284349    29.457  < 2e-16 ***
ORIGIN_SZ1646  3.5931982  0.1285792    27.945  < 2e-16 ***
ORIGIN_SZ1647  3.9788139  0.1284222    30.982  < 2e-16 ***
ORIGIN_SZ1648  4.5988103  0.1283876    35.820  < 2e-16 ***
ORIGIN_SZ1649  5.3718355  0.1283546    41.852  < 2e-16 ***
ORIGIN_SZ1650  5.4873773  0.1284050    42.735  < 2e-16 ***
ORIGIN_SZ1664 -0.5466103  0.1813269    -3.015 0.002574 ** 
ORIGIN_SZ1665  4.6877073  0.1283604    36.520  < 2e-16 ***
ORIGIN_SZ1666  3.4062823  0.1284771    26.513  < 2e-16 ***
ORIGIN_SZ1667  4.4232882  0.1286615    34.379  < 2e-16 ***
ORIGIN_SZ1668  4.5318630  0.1283819    35.300  < 2e-16 ***
ORIGIN_SZ1670  5.4088882  0.1283477    42.142  < 2e-16 ***
ORIGIN_SZ1671  6.0838254  0.1284023    47.381  < 2e-16 ***
ORIGIN_SZ1672  5.7049441  0.1284293    44.421  < 2e-16 ***
ORIGIN_SZ1684  3.7187181  0.1288702    28.856  < 2e-16 ***
ORIGIN_SZ1685  4.2555448  0.1284035    33.142  < 2e-16 ***
ORIGIN_SZ1686  4.1437766  0.1284031    32.272  < 2e-16 ***
ORIGIN_SZ1687  3.6993537  0.1285034    28.788  < 2e-16 ***
ORIGIN_SZ1688  3.2422176  0.1285630    25.219  < 2e-16 ***
ORIGIN_SZ1689  2.8871351  0.1288455    22.408  < 2e-16 ***
ORIGIN_SZ1690  4.2769664  0.1284599    33.294  < 2e-16 ***
ORIGIN_SZ1691  5.0966925  0.1283750    39.702  < 2e-16 ***
ORIGIN_SZ1692  4.6944612  0.1285417    36.521  < 2e-16 ***
ORIGIN_SZ1706  4.2405145  0.1284411    33.015  < 2e-16 ***
ORIGIN_SZ1707  4.1267925  0.1283945    32.141  < 2e-16 ***
ORIGIN_SZ1708  4.6515595  0.1283637    36.237  < 2e-16 ***
ORIGIN_SZ1709  3.7700021  0.1284598    29.348  < 2e-16 ***
ORIGIN_SZ1710  4.9670420  0.1283684    38.694  < 2e-16 ***
ORIGIN_SZ1711  4.7983231  0.1283920    37.372  < 2e-16 ***
ORIGIN_SZ1712  5.4136434  0.1283471    42.180  < 2e-16 ***
ORIGIN_SZ1713  3.0125277  0.1288959    23.372  < 2e-16 ***
ORIGIN_SZ1714  5.6442978  0.1283871    43.963  < 2e-16 ***
ORIGIN_SZ1727  4.4574547  0.1284012    34.715  < 2e-16 ***
ORIGIN_SZ1728  4.3351186  0.1283855    33.766  < 2e-16 ***
ORIGIN_SZ1729  3.7785773  0.1284218    29.423  < 2e-16 ***
ORIGIN_SZ1730  1.7369592  0.1300694    13.354  < 2e-16 ***
ORIGIN_SZ1731  4.6338734  0.1283936    36.091  < 2e-16 ***
ORIGIN_SZ1732  5.0905241  0.1283553    39.660  < 2e-16 ***
ORIGIN_SZ1733  4.8477092  0.1283778    37.761  < 2e-16 ***
ORIGIN_SZ1734  5.2568117  0.1283742    40.949  < 2e-16 ***
ORIGIN_SZ1735  6.9689832  0.1284616    54.250  < 2e-16 ***
ORIGIN_SZ1748  3.1734114  0.1286335    24.670  < 2e-16 ***
ORIGIN_SZ1749  4.1468003  0.1283953    32.297  < 2e-16 ***
ORIGIN_SZ1750  3.2613612  0.1284986    25.381  < 2e-16 ***
ORIGIN_SZ1751  2.5480666  0.1287617    19.789  < 2e-16 ***
ORIGIN_SZ1753  5.1283339  0.1283607    39.953  < 2e-16 ***
ORIGIN_SZ1754  5.5104972  0.1283459    42.935  < 2e-16 ***
ORIGIN_SZ1755  5.0221300  0.1283760    39.120  < 2e-16 ***
ORIGIN_SZ1756  4.9811190  0.1284102    38.791  < 2e-16 ***
ORIGIN_SZ1757  2.9497619  0.1319618    22.353  < 2e-16 ***
ORIGIN_SZ1769  3.9626587  0.1284323    30.854  < 2e-16 ***
ORIGIN_SZ1770  3.9969946  0.1285514    31.093  < 2e-16 ***
ORIGIN_SZ1771  2.7783443  0.1286934    21.589  < 2e-16 ***
ORIGIN_SZ1772  1.6643605  0.1304154    12.762  < 2e-16 ***
ORIGIN_SZ1774  4.8462943  0.1283722    37.752  < 2e-16 ***
ORIGIN_SZ1775  4.5115076  0.1284142    35.132  < 2e-16 ***
ORIGIN_SZ1776  5.7008216  0.1283497    44.416  < 2e-16 ***
ORIGIN_SZ1777  5.7202295  0.1283656    44.562  < 2e-16 ***
ORIGIN_SZ1778  5.5268171  0.1288405    42.897  < 2e-16 ***
ORIGIN_SZ1790  4.6407250  0.1283929    36.145  < 2e-16 ***
ORIGIN_SZ1791  4.0003425  0.1284480    31.144  < 2e-16 ***
ORIGIN_SZ1792  3.9251321  0.1284655    30.554  < 2e-16 ***
ORIGIN_SZ1793  2.0307331  0.1289694    15.746  < 2e-16 ***
ORIGIN_SZ1794  1.7992380  0.1310605    13.728  < 2e-16 ***
ORIGIN_SZ1795  1.3069606  0.1322365     9.884  < 2e-16 ***
ORIGIN_SZ1796  5.3162956  0.1283742    41.412  < 2e-16 ***
ORIGIN_SZ1797  5.3447045  0.1283626    41.638  < 2e-16 ***
ORIGIN_SZ1798  5.3785600  0.1283640    41.901  < 2e-16 ***
ORIGIN_SZ1799  4.6072423  0.1285228    35.848  < 2e-16 ***
ORIGIN_SZ1800  3.9498043  0.1308451    30.187  < 2e-16 ***
ORIGIN_SZ1811  3.7138890  0.1284970    28.903  < 2e-16 ***
ORIGIN_SZ1812  4.8789898  0.1283529    38.012  < 2e-16 ***
ORIGIN_SZ1813  4.6561018  0.1283626    36.273  < 2e-16 ***
ORIGIN_SZ1817  5.4056473  0.1283943    42.102  < 2e-16 ***
ORIGIN_SZ1818  5.1927141  0.1283798    40.448  < 2e-16 ***
ORIGIN_SZ1819  5.7273655  0.1283578    44.620  < 2e-16 ***
ORIGIN_SZ1820  2.8647670  0.1327721    21.577  < 2e-16 ***
ORIGIN_SZ1832  4.5074899  0.1284059    35.103  < 2e-16 ***
ORIGIN_SZ1833  3.9377954  0.1284330    30.660  < 2e-16 ***
ORIGIN_SZ1834  4.2644257  0.1283825    33.217  < 2e-16 ***
ORIGIN_SZ1835  3.5659499  0.1285070    27.749  < 2e-16 ***
ORIGIN_SZ1837  0.7690953  0.1419186     5.419 5.98e-08 ***
ORIGIN_SZ1839  4.6358637  0.1284983    36.077  < 2e-16 ***
ORIGIN_SZ1840  6.4716119  0.1283366    50.427  < 2e-16 ***
ORIGIN_SZ1841  2.2983709  0.1330375    17.276  < 2e-16 ***
ORIGIN_SZ1842  6.4694885  0.1287331    50.255  < 2e-16 ***
ORIGIN_SZ1853  4.3256678  0.1283955    33.690  < 2e-16 ***
ORIGIN_SZ1854  4.5606620  0.1283856    35.523  < 2e-16 ***
ORIGIN_SZ1855  4.8503696  0.1283699    37.784  < 2e-16 ***
ORIGIN_SZ1858  2.6470639  0.1307361    20.247  < 2e-16 ***
ORIGIN_SZ1860  5.9892312  0.1285733    46.582  < 2e-16 ***
ORIGIN_SZ1861  5.4449058  0.1283857    42.411  < 2e-16 ***
ORIGIN_SZ1874  4.5098276  0.1284380    35.113  < 2e-16 ***
ORIGIN_SZ1875  2.8330493  0.1289053    21.978  < 2e-16 ***
ORIGIN_SZ1876  4.9442722  0.1287017    38.417  < 2e-16 ***
ORIGIN_SZ1877  4.5626564  0.1283895    35.538  < 2e-16 ***
ORIGIN_SZ1880  0.9829313  0.1365106     7.200 6.00e-13 ***
ORIGIN_SZ1882  5.2992540  0.1283965    41.273  < 2e-16 ***
ORIGIN_SZ1883  5.8024625  0.1285970    45.121  < 2e-16 ***
ORIGIN_SZ1895  4.6351599  0.1283881    36.103  < 2e-16 ***
ORIGIN_SZ1896  2.9955843  0.1286416    23.286  < 2e-16 ***
ORIGIN_SZ1897  3.6604153  0.1285855    28.467  < 2e-16 ***
ORIGIN_SZ1898 -0.6599083  0.1778219    -3.711 0.000206 ***
ORIGIN_SZ1901  0.7749620  0.1467246     5.282 1.28e-07 ***
ORIGIN_SZ1903  5.1887292  0.1285909    40.351  < 2e-16 ***
ORIGIN_SZ1917  3.2192269  0.1286185    25.029  < 2e-16 ***
ORIGIN_SZ1918  4.6602616  0.1284272    36.287  < 2e-16 ***
ORIGIN_SZ1919  4.5380961  0.1284026    35.343  < 2e-16 ***
ORIGIN_SZ1922  2.3087644  0.1312319    17.593  < 2e-16 ***
ORIGIN_SZ1924  5.0214296  0.1286230    39.040  < 2e-16 ***
ORIGIN_SZ1937  4.0309239  0.1284751    31.375  < 2e-16 ***
ORIGIN_SZ1938  4.6755113  0.1283771    36.420  < 2e-16 ***
ORIGIN_SZ1939  5.2285909  0.1283681    40.731  < 2e-16 ***
ORIGIN_SZ1942  1.2796556  0.1345281     9.512  < 2e-16 ***
ORIGIN_SZ1959  3.6051332  0.1285704    28.040  < 2e-16 ***
ORIGIN_SZ1960  5.5903041  0.1283372    43.559  < 2e-16 ***
ORIGIN_SZ1961  3.9886969  0.1284784    31.046  < 2e-16 ***
ORIGIN_SZ1962  5.0143993  0.1283745    39.061  < 2e-16 ***
ORIGIN_SZ1964  0.2513609  0.1525944     1.647 0.099507 .  
ORIGIN_SZ1979  3.9080186  0.1285324    30.405  < 2e-16 ***
ORIGIN_SZ1980  2.1544333  0.1290272    16.698  < 2e-16 ***
ORIGIN_SZ1981  4.6365812  0.1283758    36.117  < 2e-16 ***
ORIGIN_SZ1982  3.4508601  0.1287496    26.803  < 2e-16 ***
ORIGIN_SZ1983  4.9242564  0.1283778    38.358  < 2e-16 ***
ORIGIN_SZ1984  3.6431087  0.1285296    28.345  < 2e-16 ***
ORIGIN_SZ1985  4.4345906  0.1284509    34.524  < 2e-16 ***
ORIGIN_SZ2001  4.2184167  0.1284302    32.846  < 2e-16 ***
ORIGIN_SZ2002  4.7630499  0.1283596    37.107  < 2e-16 ***
ORIGIN_SZ2003  4.3973471  0.1283983    34.248  < 2e-16 ***
ORIGIN_SZ2004  5.0199149  0.1283720    39.104  < 2e-16 ***
ORIGIN_SZ2005  4.8956048  0.1283712    38.136  < 2e-16 ***
ORIGIN_SZ2006  3.4575991  0.1286229    26.882  < 2e-16 ***
ORIGIN_SZ2007  2.8498303  0.1292845    22.043  < 2e-16 ***
ORIGIN_SZ2022  4.5952513  0.1284300    35.780  < 2e-16 ***
ORIGIN_SZ2023  5.0117105  0.1283577    39.045  < 2e-16 ***
ORIGIN_SZ2024  4.3242920  0.1283898    33.681  < 2e-16 ***
ORIGIN_SZ2025  4.3546802  0.1283861    33.919  < 2e-16 ***
ORIGIN_SZ2026  3.0208249  0.1287979    23.454  < 2e-16 ***
ORIGIN_SZ2027  5.3158698  0.1283666    41.412  < 2e-16 ***
ORIGIN_SZ2043  3.9075284  0.1285194    30.404  < 2e-16 ***
ORIGIN_SZ2044  4.6274993  0.1283729    36.047  < 2e-16 ***
ORIGIN_SZ2045  0.3537318  0.1435921     2.463 0.013761 *  
ORIGIN_SZ2046  4.5807504  0.1283630    35.686  < 2e-16 ***
ORIGIN_SZ2047  4.3432419  0.1284089    33.824  < 2e-16 ***
ORIGIN_SZ2048  4.6367218  0.1283862    36.115  < 2e-16 ***
ORIGIN_SZ2049  3.7174760  0.1289577    28.827  < 2e-16 ***
ORIGIN_SZ2064  4.5752841  0.1283961    35.634  < 2e-16 ***
ORIGIN_SZ2065  3.0666127  0.1285674    23.852  < 2e-16 ***
ORIGIN_SZ2066  2.4252096  0.1303253    18.609  < 2e-16 ***
ORIGIN_SZ2067  5.8329188  0.1283346    45.451  < 2e-16 ***
ORIGIN_SZ2068  4.1693543  0.1284817    32.451  < 2e-16 ***
ORIGIN_SZ2069  4.5189874  0.1284176    35.190  < 2e-16 ***
ORIGIN_SZ2085  3.4872368  0.1286312    27.110  < 2e-16 ***
ORIGIN_SZ2086  4.9165833  0.1283673    38.301  < 2e-16 ***
ORIGIN_SZ2087  3.5650820  0.1284901    27.746  < 2e-16 ***
ORIGIN_SZ2088  4.2418364  0.1283844    33.040  < 2e-16 ***
ORIGIN_SZ2089  3.9807971  0.1284591    30.989  < 2e-16 ***
ORIGIN_SZ2090  5.5293310  0.1283511    43.080  < 2e-16 ***
ORIGIN_SZ2091  0.9136463  0.1430196     6.388 1.68e-10 ***
ORIGIN_SZ2105  1.6527954  0.1617990    10.215  < 2e-16 ***
ORIGIN_SZ2106  1.8173872  0.1296309    14.020  < 2e-16 ***
ORIGIN_SZ2107  3.0072150  0.1285965    23.385  < 2e-16 ***
ORIGIN_SZ2108  4.2092619  0.1284188    32.778  < 2e-16 ***
ORIGIN_SZ2109  4.2850041  0.1283829    33.377  < 2e-16 ***
ORIGIN_SZ2110  3.7216005  0.1285029    28.961  < 2e-16 ***
ORIGIN_SZ2111  1.1562654  0.1339491     8.632  < 2e-16 ***
ORIGIN_SZ2128  2.6600982  0.1290106    20.619  < 2e-16 ***
ORIGIN_SZ2129  2.0823288  0.1291362    16.125  < 2e-16 ***
ORIGIN_SZ2130  4.7533655  0.1283628    37.031  < 2e-16 ***
ORIGIN_SZ2131  5.0766995  0.1283819    39.544  < 2e-16 ***
ORIGIN_SZ2132  4.0403178  0.1284398    31.457  < 2e-16 ***
ORIGIN_SZ2148  3.5612816  0.1287767    27.655  < 2e-16 ***
ORIGIN_SZ2149  2.1561798  0.1291392    16.697  < 2e-16 ***
ORIGIN_SZ2150  4.6576297  0.1283840    36.279  < 2e-16 ***
ORIGIN_SZ2151  5.1132952  0.1283533    39.838  < 2e-16 ***
ORIGIN_SZ2152  5.3033728  0.1283595    41.317  < 2e-16 ***
ORIGIN_SZ2153  4.6356684  0.1284211    36.097  < 2e-16 ***
ORIGIN_SZ2171  3.6332254  0.1284957    28.275  < 2e-16 ***
ORIGIN_SZ2172  3.7323010  0.1285285    29.039  < 2e-16 ***
ORIGIN_SZ2173  4.2773750  0.1284030    33.312  < 2e-16 ***
ORIGIN_SZ2174  4.5619158  0.1284115    35.526  < 2e-16 ***
ORIGIN_SZ2191  3.1114873  0.1287109    24.174  < 2e-16 ***
ORIGIN_SZ2192  3.0217062  0.1287488    23.470  < 2e-16 ***
ORIGIN_SZ2193  3.9655386  0.1284480    30.873  < 2e-16 ***
ORIGIN_SZ2194  4.4091324  0.1284040    34.338  < 2e-16 ***
ORIGIN_SZ2195  3.7733700  0.1298799    29.053  < 2e-16 ***
ORIGIN_SZ2212  0.8098237  0.1525904     5.307 1.11e-07 ***
ORIGIN_SZ2213  1.0782767  0.1333223     8.088 6.08e-16 ***
ORIGIN_SZ2214  1.4668123  0.1310108    11.196  < 2e-16 ***
ORIGIN_SZ2215  4.0983377  0.1284767    31.899  < 2e-16 ***
ORIGIN_SZ2216  3.0542160  0.1287556    23.721  < 2e-16 ***
ORIGIN_SZ2233  1.0944048  0.1356535     8.068 7.17e-16 ***
ORIGIN_SZ2234  2.9061998  0.1298025    22.389  < 2e-16 ***
ORIGIN_SZ2235  2.9341792  0.1289298    22.758  < 2e-16 ***
ORIGIN_SZ2236  2.8109067  0.1289231    21.803  < 2e-16 ***
ORIGIN_SZ2237  0.6457632  0.1399946     4.613 3.97e-06 ***
ORIGIN_SZ2256  0.5871896  0.1350322     4.349 1.37e-05 ***
ORIGIN_SZ2257  2.5703596  0.1297101    19.816  < 2e-16 ***
ORIGIN_SZ2258  2.1509525  0.1292432    16.643  < 2e-16 ***
ORIGIN_SZ2259  1.8622755  0.1325604    14.049  < 2e-16 ***
ORIGIN_SZ2277  2.6688346  0.1334693    19.996  < 2e-16 ***
ORIGIN_SZ2278  3.7780627  0.1288226    29.328  < 2e-16 ***
ORIGIN_SZ2279  1.7018214  0.1298144    13.110  < 2e-16 ***
ORIGIN_SZ2280 -0.2289202  0.1646950    -1.390 0.164540    
ORIGIN_SZ2297  4.6422258  0.1286067    36.096  < 2e-16 ***
ORIGIN_SZ2300  0.3937649  0.1449787     2.716 0.006607 ** 
ORIGIN_SZ2301  2.1079027  0.1296113    16.263  < 2e-16 ***
ORIGIN_SZ2318  2.6638788  0.1295632    20.560  < 2e-16 ***
ORIGIN_SZ2319  3.3334151  0.1287048    25.900  < 2e-16 ***
ORIGIN_SZ2322  3.3271113  0.1288204    25.828  < 2e-16 ***
ORIGIN_SZ2337  4.2216265  0.1294297    32.617  < 2e-16 ***
ORIGIN_SZ2341  3.8112749  0.1286292    29.630  < 2e-16 ***
ORIGIN_SZ2343  2.5327363  0.1290309    19.629  < 2e-16 ***
ORIGIN_SZ2361  3.4319983  0.1288172    26.642  < 2e-16 ***
ORIGIN_SZ2364 -0.4204127  0.1478177    -2.844 0.004453 ** 
ORIGIN_SZ2379  3.3699803  0.1298850    25.946  < 2e-16 ***
ORIGIN_SZ2384  2.5353185  0.1291383    19.633  < 2e-16 ***
ORIGIN_SZ2405  2.2192627  0.1291656    17.182  < 2e-16 ***
ORIGIN_SZ2406  0.9149560  0.1323648     6.912 4.77e-12 ***
ORIGIN_SZ2426  1.7730999  0.1309198    13.543  < 2e-16 ***
ORIGIN_SZ2427  3.2807490  0.1287748    25.477  < 2e-16 ***
ORIGIN_SZ2505  3.7127909  0.1340928    27.688  < 2e-16 ***
DESTIN_SZ44    1.3465584  0.0552747    24.361  < 2e-16 ***
DESTIN_SZ46    0.4733805  0.0545386     8.680  < 2e-16 ***
DESTIN_SZ66   -0.3997839  0.0684168    -5.843 5.12e-09 ***
DESTIN_SZ67    0.3368221  0.0528685     6.371 1.88e-10 ***
DESTIN_SZ68    0.0845370  0.0547088     1.545 0.122293    
DESTIN_SZ86    0.4635816  0.0610670     7.591 3.17e-14 ***
DESTIN_SZ87   -3.1422407  0.0988168   -31.799  < 2e-16 ***
DESTIN_SZ88   -0.1180767  0.0538092    -2.194 0.028210 *  
DESTIN_SZ89   -0.6980253  0.0553479   -12.612  < 2e-16 ***
DESTIN_SZ90   -3.9160037  0.7091227    -5.522 3.35e-08 ***
DESTIN_SZ109  -0.6226877  0.0562075   -11.078  < 2e-16 ***
DESTIN_SZ110  -3.2079492  0.1125824   -28.494  < 2e-16 ***
DESTIN_SZ111   0.9793176  0.0521947    18.763  < 2e-16 ***
DESTIN_SZ112  -2.5128641  0.0602095   -41.735  < 2e-16 ***
DESTIN_SZ128   1.1851457  0.0558600    21.216  < 2e-16 ***
DESTIN_SZ129  -4.5074531  0.1432562   -31.464  < 2e-16 ***
DESTIN_SZ130  -0.6607416  0.0555224   -11.900  < 2e-16 ***
DESTIN_SZ131  -1.4454080  0.0555613   -26.015  < 2e-16 ***
DESTIN_SZ132  -0.9091877  0.0528203   -17.213  < 2e-16 ***
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DESTIN_SZ2111 -3.2705285  0.0608965   -53.706  < 2e-16 ***
DESTIN_SZ2128 -0.6342079  0.0518329   -12.236  < 2e-16 ***
DESTIN_SZ2129 -0.8166701  0.0521164   -15.670  < 2e-16 ***
DESTIN_SZ2130 -0.7555801  0.0514389   -14.689  < 2e-16 ***
DESTIN_SZ2131 -0.7930385  0.0516386   -15.357  < 2e-16 ***
DESTIN_SZ2132 -1.3362523  0.0517012   -25.846  < 2e-16 ***
DESTIN_SZ2148 -1.3564723  0.0532175   -25.489  < 2e-16 ***
DESTIN_SZ2149 -1.4365154  0.0522910   -27.472  < 2e-16 ***
DESTIN_SZ2150 -1.0887767  0.0518064   -21.016  < 2e-16 ***
DESTIN_SZ2151  0.5962899  0.0512590    11.633  < 2e-16 ***
DESTIN_SZ2152 -0.3742242  0.0514138    -7.279 3.37e-13 ***
DESTIN_SZ2153 -1.6780871  0.0523817   -32.036  < 2e-16 ***
DESTIN_SZ2171 -0.1744648  0.0514510    -3.391 0.000697 ***
DESTIN_SZ2172 -1.8376704  0.0523240   -35.121  < 2e-16 ***
DESTIN_SZ2173 -1.4517682  0.0516775   -28.093  < 2e-16 ***
DESTIN_SZ2174 -0.7973274  0.0515841   -15.457  < 2e-16 ***
DESTIN_SZ2191  0.0902737  0.0516998     1.746 0.080791 .  
DESTIN_SZ2192 -1.2790689  0.0522786   -24.466  < 2e-16 ***
DESTIN_SZ2193 -0.6378899  0.0515557   -12.373  < 2e-16 ***
DESTIN_SZ2194 -0.6737004  0.0514791   -13.087  < 2e-16 ***
DESTIN_SZ2195 -2.5995678  0.0623353   -41.703  < 2e-16 ***
DESTIN_SZ2212  0.0746680  0.0528250     1.413 0.157510    
DESTIN_SZ2213 -0.2507887  0.0518153    -4.840 1.30e-06 ***
DESTIN_SZ2214  0.4079463  0.0517061     7.890 3.03e-15 ***
DESTIN_SZ2215 -1.2526124  0.0520350   -24.072  < 2e-16 ***
DESTIN_SZ2216 -0.4016979  0.0515234    -7.796 6.37e-15 ***
DESTIN_SZ2233  0.4360380  0.0521165     8.367  < 2e-16 ***
DESTIN_SZ2234  0.9816535  0.0518510    18.932  < 2e-16 ***
DESTIN_SZ2235 -0.3711216  0.0519384    -7.145 8.97e-13 ***
DESTIN_SZ2236 -1.8616497  0.0529479   -35.160  < 2e-16 ***
DESTIN_SZ2237 -0.3613258  0.0524631    -6.887 5.69e-12 ***
DESTIN_SZ2256 -0.1486757  0.0526155    -2.826 0.004718 ** 
DESTIN_SZ2257 -2.6465337  0.0575364   -45.998  < 2e-16 ***
DESTIN_SZ2258 -0.6302004  0.0516952   -12.191  < 2e-16 ***
DESTIN_SZ2259  0.4493450  0.0522187     8.605  < 2e-16 ***
DESTIN_SZ2277 -1.4277992  0.0572798   -24.927  < 2e-16 ***
DESTIN_SZ2278 -1.0987939  0.0535642   -20.514  < 2e-16 ***
DESTIN_SZ2279 -0.4217723  0.0517179    -8.155 3.48e-16 ***
DESTIN_SZ2280 -1.6980359  0.0600373   -28.283  < 2e-16 ***
DESTIN_SZ2297 -1.6317059  0.0544077   -29.990  < 2e-16 ***
DESTIN_SZ2300 -1.5357290  0.0551923   -27.825  < 2e-16 ***
DESTIN_SZ2301 -0.7032192  0.0521112   -13.495  < 2e-16 ***
DESTIN_SZ2318  0.7165873  0.0514743    13.921  < 2e-16 ***
DESTIN_SZ2319  0.7156622  0.0514403    13.912  < 2e-16 ***
DESTIN_SZ2322 -0.2356355  0.0519697    -4.534 5.79e-06 ***
DESTIN_SZ2337  0.2733136  0.0544478     5.020 5.17e-07 ***
DESTIN_SZ2341  1.0100202  0.0514164    19.644  < 2e-16 ***
DESTIN_SZ2343 -1.1431043  0.0527584   -21.667  < 2e-16 ***
DESTIN_SZ2361 -0.3581483  0.0520025    -6.887 5.69e-12 ***
DESTIN_SZ2364 -2.2471011  0.0591155   -38.012  < 2e-16 ***
DESTIN_SZ2379 -1.2051440  0.0579292   -20.804  < 2e-16 ***
DESTIN_SZ2384  0.7246833  0.0515972    14.045  < 2e-16 ***
DESTIN_SZ2405  1.3975678  0.0514186    27.180  < 2e-16 ***
DESTIN_SZ2406 -1.6290299  0.0563539   -28.907  < 2e-16 ***
DESTIN_SZ2426  0.8495482  0.0523702    16.222  < 2e-16 ***
DESTIN_SZ2427  1.1361526  0.0516163    22.012  < 2e-16 ***
DESTIN_SZ2505  0.7094831  0.0546883    12.973  < 2e-16 ***
log(dist)     -1.6146098  0.0002885 -5595.605  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 101244825  on 64961  degrees of freedom
Residual deviance:  25322395  on 63326  degrees of freedom
AIC: 25684037

Number of Fisher Scoring iterations: 10

In the Destin Constrained Model, the coefficients for five variables are all NA (Not Available), meaning that suitable coefficient values could not be calculated during the model fitting process. The specific cause requires further examination

For the purpose of model comparison, we decided to exclude Destin Constrained Model. This ensures that, for a reliable comparison of model performance, the comparison is based on reliable estimates, avoiding the influence of variables with coefficients that could not be computed.

9 Model Comparison

First of all, let us create a list called model_list by using the code chunk below. It contains all our fitted models for all four variations of gravity model.

Code 
model_list <- list(
  Unconstrained = uncSIM,
  Origin_Constrained = orcSIM,
  Doubly_Constrained = dbcSIM)

Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.

The RMSE values provide a measure of the goodness of fit for each model. A lower RMSE indicates better model performance in terms of how well the model predictions align with the observed values. In this comparison, the Doubly Constrained Model has the lowest RMSE (1219.291), suggesting that it performs better in terms of minimizing prediction errors compared to the Unconstrained and Origin Constrained models.

Code 
compare_performance(model_list,
                    metrics = "RMSE")
# Comparison of Model Performance Indices

Name               | Model |     RMSE
-------------------------------------
Unconstrained      |   glm | 1773.898
Origin_Constrained |   glm | 1653.729
Doubly_Constrained |   glm | 1219.291

9.1 Visualising the fitted values

We will do a plot to visualise the observed values and the fitted values.

Firstly we will extract the fitted values from each model by using the code chunk below.

Code 
df <- as.data.frame(uncSIM$fitted.values) %>%
  round(digits = 0)

Next, we will join the values to SIM_data data frame:

Code 
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df) %>%
  rename(uncTRIPS = "uncSIM$fitted.values")

Repeat the same step by for Origin Constrained SIM:

Code 
df <- as.data.frame(orcSIM$fitted.values) %>%
  round(digits = 0)
Code 
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df) %>%
  rename(orcTRIPS = "orcSIM$fitted.values")

Repeat the same step by for Doubly Constrained SIM:

Code 
df<- as.data.frame(dbcSIM$fitted.values) %>%   
  round(digits = 0)
Code 
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df) %>%
  rename(dbcTRIPS = "dbcSIM$fitted.values")

We will create scatter plots displaying the relationship between actual and predicted values through linear fitting and compare each other.

Code 
unc_p <- ggplot(data = inter_zonal_flow,
                aes(x = uncTRIPS,
                    y = MORNING_PEAK)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,100000),
                  ylim=c(0,100000))

orc_p <- ggplot(data = inter_zonal_flow,
                aes(x = orcTRIPS,
                    y = MORNING_PEAK)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,100000),
                  ylim=c(0,100000))

dbc_p <- ggplot(data = inter_zonal_flow,
                aes(x = dbcTRIPS,
                    y = MORNING_PEAK)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,100000),
                  ylim=c(0,100000))

ggarrange( unc_p, orc_p, dbc_p,
          ncol = 2,
          nrow = 2)

The results indicate that for the Doubly Constrained Model, the scatter plot points closely follow the fitted curve. This tight distribution suggests strong linear correlation between the actual values and the model predictions. The model appears to accurately capture the variation trends in the actual values, making it well-suited for describing underlying relationships.

10 Conclusion

In the comparison of three spatial interaction models (UNC, ORC, DBC), insights are provided through the examination of R-squared values. Specifically, the DBC model stands out with an R-squared value of 59%, signifying superior explanatory power among the considered models. Additionally, the comparison of Root Mean Square Error (RMSE) reveals that the DBC model has the lowest RMSE at 1219.291. This implies that the DBC model demonstrates the least average deviation in predictions compared to observed values, showcasing higher predictive accuracy.

According to the UNC and ORC models, the p-values of all the variables are very small (<0.05) , indicating that their contributions in the models are highly statistically significant. Considering both models, Entertainment consistently emerges as the variable with the most significant positive impact, followed by School and HDB. Distance consistently exhibits the most significant negative impact in both the UNC and ORC models.